The memory, if you are gaming below 1920x1080 512MB is fine, for 1920x1080 and up you should have 1GB, and if you want to play at 2560x1600 with 8x AA you will get a boost from 2GB. Most of the newer cards now come with 1GB so you dont really need to pay much attention to it.
And the name of the card, eg 5770, GTX 260 etc. nVidia has had a few exceptions(GTX260 192 vx GTX260 216) but in general the cards of the same name are identical, some OEMs will OC the card but they will charge you significantly more for it.
When you are considering buying a card, figure out your budget, figure out what cards are in your budget, you can browse newegg or check out best cards for the money, then look at some benchmarks for specific games that you are considering playing and go off of them.
We have made it to the day when it is very hard to determine how a card will perform based off of its specs alone and nVidia and ATI SP's perform very differently, so while the GTX285 has 240SPs and the 5850 has 1440SPs they actually perform equally.
Or you can always list your system specs, your budget, and the resolution you plan to use and we can let you know what your best options are. If you want to go out and buy one on your own by trying to understand the numbers, it can get quite confusing. As hunter315 said, the numbers between ATi and nVidia cards are not interchangeable.