Both allow customization of your convo screen and I think he message list as well (I know chomp does).
Handcent, if memory serves, give the option of different chat styles, while chomp only allows bubbles. You can change the bubble color to match the background, but your texts will be on one side (left or right) and whoever texts you will be on the other. I forget which is which.
If you use Facebook sync, and have any contacts whose numbers come ONLY from there, they don't show up in chomp. I emailed the dev. Their fix is to remove sync with facebook, add that person to your contacts, then turn facebook sync back on.
I used chomp longer than handcent, but in the long run, decided the stock messaging was good enough and didn't see the need to have a secondary app taking up space and etc.
If you really want to use one, I'd give each one a try for at least a couple days, if not longer, and choose for yourself.
I believe the stock messaging holds your texts in memory either way, but you should check that and backup any hat are important to be sure you keep them.
Let us know what you think if you them both!