Which is better/uses less memory/gives you less problems...for those of you that have had both...I had Chomp I think on my G1 a couple years ago....but don't see much of a difference from just looking at them.
I found them to be very similar ... handcent had a bit more customization so I chose that one (notifications for individual text such as led flashing in various colors, and the icon that appears in the notification bar - handcent allowed for me to customize my husband's texts with one color and my kids with others)
Some people have reported that Chomp is less buggy ...
I'd say give each a try for a few days to see which you prefer but they are very similar and both work well.
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.
I like the stock messaging application, but I like the ability to do batch jobs. I also like how Handcent wakes the phone and gives me a popup. Does Chomp do the popup thing?