I only really have experience with colour Tamas, so I apologise, but here are my thoughts and experiences with them.
iD L(E) - I have the English version but, as far as I am aware, it is exactly the same as the Japanese language version, bar the language (obviously) and a few favourite items. The iD L(E) has two in built games;
Hamburger and
Run and Jump. In
Hamburger you play as Kuchipatchi and you have to try and eat all of the burgers on the plate, while avoiding the 'problematic skulls' (this is the actual translation in the English manual!). Basically, Kuchipatchi jumps from item to item and you have to 'eat' only when he's at a burger. It's quite challenging and took me months to get a perfect score on it! I really enjoy it though.
Run and Jump is pretty much what it suggests; you play as Mametchi and you're running along a little track and have to avoid the obstacles by jumping over them and jumping up to collect the coins. Highly addictive and extremely fun; this is both mine and my boyfriend's favourite of all the Tamagotchi games we have played. Out of all of the devices, this is my favourite for in built games (it happens to also be my favourite device full stop, but that's besides the point). If you're looking for good in built games I'd definitely recommend this model; plus, it connects with the P's, which you already have!
iD L 15th Anniversary Ver. - I specifically bought this model because the games looked so interesting and different; like the iD L(E), it has two built in games. These games are
Sliding Puzzle and
Maze.
Sliding Puzzle is one of those puzzles where there are nine tiles and you have to move them around to complete the image. I happen to be pretty good at visual logic puzzles (I just 'know' where to put things; there's one particular logic puzzle, Rush Hour (and variants thereof), which everyone is always amazed at just how quickly I can do. Not that that has anything to do with Tamagotchis), so I can complete this game fairly easily and thus enjoy it. However, my boyfriend (who is truly
awful at visual logic puzzles and he would agree) hates this games and really struggles with it.
Maze is, as you'd expect, a maze. This is probably the most complex game I've ever found on a Tamagotchi. You play as either Mametchi or Lovelitchi and you ahve to complete the maze while picking up all of the hearts and avoiding a fly. It's
hard. It would be much better if the fly moved more logically (e.g., if it could only move one square instead of being able to appear anywhere in the maze), but it is what it is. I enjoy it, although I find it extremely frustrating at times; my boyfriend is less keen. Also, unlike all the other models I've encounter
Maze is the one game which awards 400G as it's top prize (although you'll be lucky to get there!). I do enjoy both of the games and think they're some of the most interesting on any colour Tama, but I feel that I've had to download some easy games on to it for those times when I just need to earn quick G; this is unlike the iD L(E), where I was content with the two in built games for over two years (and even now play those over the downloads). However, the 15th Anni. Ver. is pretty expensive for a couple of mini games, so although they're incredibly fun, I probably wouldn't recommend this model unless you were either a) wanting it for collection purposes or
like all of the other features enough (e.g., the vintage raisable characters).
P's - I know you already have this, so instead I'll talk about the games on the Pierces that I have. As an aside, I think the two in built games are alright but a little repetative.
Love & Melody - A catching game. There are a bunch of items at the side of the screen, which you have to collect. Three objects will fall from the top of the screen and you have to catch the correct one (e.g., there will be a pink, blue and yellow music note and at the side you'll see a blue one). It's quite fun this one, I do enjoy it although I haven't played it much as I happened to have the same game (with different visuals) already downloaded onto my P's at this point!
Star Circus - In this game you get an animation of Mametchi (dressed as a clown) balancing on a ball, while spinning plates; after a short period he'll stop and you have to press the 'A' button if he stops on the left, and the 'B' button if he stops on the right. If he's balancing two plates at one time you hit the button twice. This game is very easy but goes on
forever. Although I love this pierce, this is easily my least favourite game; I'd enjoy it far more if it only took half as long.
MelodyLand - There's a row of music themed Tamas who all jump up and down; when the far left Tama jumps up you press the 'A' button, when the far right Tama jumps up you press the 'B' button (and don't press anything for any of the Tamas in between). I like this one; it's simple, but it's built really well, plus I like the animations.
Berry Sweets - Cake decorating! Another simple game and, to be honest, it's not particularly fun, but the animations are cute and it's less time consuming than the above. In this, you mash the 'A' button (or is it 'B'? I forget) as many times as you can in X amount of seconds in an attempt to fill up the bar; the fuller it is when time is up, the more Gotchi Points you get.
Miracrise - Another catching game, but different to above. In this, there is a dress made of four pieces at the side of the screen. You then have to assemble this dress by catching all of the different components (e.g., catch the blue skirt, followed by the purple belt, followed by the pink top) while avoiding catching the wrong pieces. This game is good fun but, as I'm sure you know, Miracrise is horribly expensive. However, there is a version of this game (different visuals) available for download; it's more challenging, in my opinion, although whether that's a good thing or not I couldn't say.
4U+ - Two built in games!
Bamboo and
Cake Making.
Bamboo is essentially a gambling game; you get three bamboo trees and you have to pick one to cut down; one will have gold, one will have creatures and one will have... I don't know, the bamboo ctter goes to sleep and says something in Japanese, so I honestly have no idea. If you select the gold three (or sleep?) three times, you get full Gotchi Points! Pick one with the creatures and you lose. It's a fun game but not so easy for earning Gotchi Points quickly. Cake Making it sort of a memory game; you have Patitchi on one side and Decoratchi on the other; they will then get out milk and cheese and you have to press the 'A' and 'B' buttons in the order they came out (so if Patitchi gets cheese out, the Decoratchi gets two milk out, followed by Patitchi getting another cheese out, it would go 'A, B, B, A'). The gambling game is quite fun actually, and I do enjoy it.
M!X - There are four in builts games on the M!X, but I haven't been unable to unlock one of them (I need to connect to three other M!Xes).
Rainbow and
Star Catch are in the arcade and
Lightning is in Rainbow Hills (the fourth game, I believe, is in Mermaid Palace).
Rainbow is something that I haven't seen on a Tama before; unsuprisingly enough, there is a rainbow, then one of the colours will disappear and you have to select the correct mix from the red, yellow and blue paint pots (e.g., if orange disappears, you select red and yellow; if a primary colour disappears, you select it twice). This one is quite enjoyable.
Star Catch sees your character running around trying to catch stars; the animation will stop at one point and (I believe it says) 'catch' will appear on the screen; you have to hit the button that corresponds with which side of the screen they have stopped on (i.e., press 'A' if they stop on the left and 'B' if they stop on the right). Sometimes they will try to catch a UFO, in which case you press the button twice. The animations for this are gorgeous, which is good as, I personally, find the game a little repetative and (just like the Star Circus counterpart) quite repetative.
Lightning is a dodging game. There are three clouds at the top and two will shoot lightning down at the Tama below. You have to move your Tama into the free space and not get struck. I really like this one; probably my favourite on the M!X; it's just a pain that you have to visit the town every time you want to play it and can't just select it from the aracade menu (so you have to watch all of the animations again; you can't just select it from the menu straight away like you can in the arcade).
Downloads - I'm not going to go through all of the downloads as there are a lot! I do find that they add to certain models though (particularly the iD L 15th Anniversary Version and the P's). I
believe that Binary has converted all of the iD and iD L downloadable games to run on the P's (as well as it's own downloadable games), so it has the greatest variety. I think you can only play iD and iD L games on the iD L(E) and only iD games on the iD. I may be wrong here. A lot of the games are the same with different visuals, although it is worth trying different ones as some are harder/easier, take more/less time or run more/less fluidly. As I've already mentioned, some of the games on the pierces are available as downloads, just with different 'skins' (Love & Melody, Star Circus, Berry Sweet and Miracrise). I think I have manages to sort it so, over all of my Tamas, I have no repeats. the iD L(E)/15th Anniversary Ver. and P's can both have two downloaded games at a time (they do not replace the in built games, nor can you remove the in built games), for a total of four games. You can have up to five games on the P's if you have two downloaded and a pierce with a game attached. The 4U+ also has downloadable games; there's a few but much less than what is available for the iD L or P's. The 4U+ mostly relies on downloads full stop though, so it didn't feel like too big a problem adding new games. I think the download limit for this is also two. I think there are also downloadable games for the M!X but (as of yet; possibly never) these are not available outside of Japan as they can only be downloaded in store and not over the internet or via an app.
I have downloads on all of my colour Tamas (excluding the M!Xes), but feel that the iD L(E) doesn't
need them. The P's doesn't need them either if you have a nice selection of pierces, but if you don't the downloads add a load of new content for free, which is nice. As much as I love the games on the iD L 15th Anniversary Version, they're so hard that I felt I did need to add some easier games for when I needed to make Gotchi Points quickly. The 4U+ benefits from downloaded games, but then, the entire model is designed to be full of downloads. Although I cannot get downloads for the M!X, I personally would add some new games as I feel that I get bored of them quite quickly.
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Phew! Sorry for the small essay! I hope this helps a little! If you have any more questions, feel free to ask and I will do my best to answer! ^_^