I think they're amazing! I wrote a guide to them and I'll copy and paste it here:
Littlest Pet Shop Digi-Pets are fun little toys full of games. The pets never die, which is pretty good! There are three versions and I have one of each; a cat version 1, a butterfly version 2, and a squirrel version 3. Here's a photo of them:
Version 1 (left) - Explore the Littlest Pet Shop world and make friends with all the pets to fill the friendship meter. Use the bottom left button to select where to go/which object to interact with and press the bottom right button to confirm. The top buttons (shaped like a mouse and a fish on my cat one) start a quick game that boosts your pet's health whenever you need to. You cannot, however, boost your pet's happiness and cleanliness whenever you want; you need to find food bowls and brushes and interact with them in order to do this. If one of your pet's stats is empty it will refuse to play games. There are many games and places to explore. Meet all the pets to unlock a special animation!
Version 2 (right) - Basically the same as Version one but instead of meeting all the pets, you need to find all your friends (which will be the same species as your pet) who have escaped from the pet shop. It's a little more challenging than Version 1 because you will not be able to see the pets you are looking for; it will play a sound when one is close by and you have to interact with certain objects in order to find them. It has the same games and places as Version 1 but different sound; also, you can now tend to your pet's needs whenever you want instead of having to find certain items. There are two plastic figures attached to strings on the virtual pet and you can insert them into the slots at the sides to make your pet happy and fed.
Version 3 (middle) - Not as fun as the other ones but it has different-shaded pixels like on the Tama-Go, and good sound effects and music In this one you do not need to look after the pet at all, and there is less exploration. You need to find your pet's friend by slowly progressing up the floors of the hotel. To get to the next floor you need to get enough coins; do this by finding coins lying around or playing games. There are different games on each floor of the hotel. Use the ears on the top of the virtual pet to control your pet, and press the body to confirm (play a game or get a coin). Press the little button on its forehead to see a cute close up of your pet. Not as interactive as it predecessors but still appealing.