There are positives and negatives to both of them for me, so it's rather hard to pick which one I'd actually prefer.
With Tamagotchis, they're small and made for traveling around. I can slide a few into my pocket and take them to work or anywhere else with me. There's also a greater variety of characters to get on the same version, or if I want a particular character, I know how to get them. (With my Digimon virtual pet, I like having Greymon, so I know exactly how to take care of him to always have him.) The downsides of Tamagotchis include the fact that they're not easy to ignore. I either have to pause them or take out the battery if I don't feel like taking care of them for a long while. It's also hard to stay attached to the character you raise, as they leave in around a week.
But with Furbies, it's easier to get attached to them. I've had the same Furby for almost a year now, and he's still the same as ever. Same with the other Furbies I have. What I like about Furbies is how much fun they are to cuddle with. While watching videos online, I can just hold a Furby and pet them, making them and myself feel better. There's also the fact that Furbies can be ignored easier, so long as no one rocks the surface they're on! Four of my Furbies haven't been touched in a while, but they're fine with that and so am I. The downside with them, though, is that it's so difficult to bring them around anywhere. If I want to, then I have to carry around a screwdriver and take the batteries in and out, depending on where I am. Which defeats the point of carrying around a Furby, as I'm just carting around the shell and not the Furby as I'm used to using them.
So really, for me, I can't pick just one. They both have their positives and negatives, and it really depends on what I'm looking for from either or what my mood is.