After Effects is not an ideal character animation tool, but if you already know the program you can make some pretty good animations with only a small amount of hair pulling and sanity questioning involved.
I’ve been creating animation style things in AE for a couple of years and it has its ups and downs. For simple transforms of limbs or characters(rotation, movement etc) its great, but you need loads of layers, and it’s quite easy to get confused with whats what. Also any complex scene requiring different drawings for poses or many mouth shapes or hand movements are annoying to set up, and not intuitive to animate. (Best method BTW is the time remapping system as shown in one of the awesome Cow Podcasts.) The puppet tool has made things much easier, but you’ll need to fiddle a bit to understand how it works, and it occasionally won’t work in any sensible manner just to annoy you. AEs obvious abilities with cameras, lights and 3d layers however can make some impressive effects very easy to achieve, and with use of parenting, pre-composing and (optionally) basic scripting can animate things incredibly fast when you get going.
I must admit when I bought the production package of CS3 I was intending to start doing this type of thing in Flash, as it’s more suited to animation projects, and seems a more sensible tool for the work. As it was I found flash utterly confusing and lacking (Or I couldn’t find) features I use a lot, so I’ve stuck with AE. If you know and can use flash I’d guess the combination of the both of them would be a perfect match (especially as you can use illustrator art for both) so you can do different scenes in which ever program you feel would be easiest for the animation/motion in that scene. (I’ll be trying my hand again with flash at some point so I can do this, as it does have many advantages for this kinda work).
Essentially, you should go with what you know best/which program you think will work best for what you want to do. If you have a lynda.com account (or money to spare) it might be worth watching their animating characters series; I watched a few of them when I had a 30 day thing going, and picked up a couple of good tips and tricks which have proved fairly handy. (Also disagreed with the overly complex way they did some stuff, but if you’re just starting out in this style of work I’d imagine it to be very helpful.)