Though both do pay you nearly nothing for used games, EB Games tends to give more in-store credit for those who wish to do that instead of getting cold hard cash.
EB Games has a wider selection, more console support, and the customer service usually acts like customer service should, unlike GameStop where they try to sell you a bunch of extra stuff you don't need, and don't babble in your ear about their personal opinions.
EB Games: Welcome. How may I assist you today?
Me: I just would like to get Battlefield 2 for PC.
EB Games: Alright, here you are, we index all of our games so we actually know what people are looking for.
Me: How much will this come to.
EB Games: Only about $10.
Me: Ah, that's nice.
EB Games: *Rings up game* Have a nice day.
Me: You too.
GameStop: YO! What are you looking for today man?
Me: Just Battlefield 2 for PC.
GameStop: Nah man, get Battlefield 2142! Way better!
Me: No, I want Battlefield 2.
GameStop: Why? It's got future weapons!
Me: I already said, I want Battlefield 2.
GameStop: Do you have an ID to verify your age?
Me: You're kidding right?
GameStop: Sorry sir, we need ID for EVERYONE who buys games rated over E.
Me: I thought it was M.
GameStop: Alright sir calm down. If you don't have an ID I can't sell you the game.
GameStop: If you buy Battlefield 2142 I will not card you. ;-)
Me: LISTEN! I do NOT want to buy Battlefield 2142! I already own it, and I want Battlefield 2. I don't care to listen to your stories about how it's so much better. JUST RING UP MY DAMN GAME!
GameStop: Do you have ID?
Me: ...FUCK YOU. I'm going to EB Games. Have fun being a virgin forever, chicks don't like guys who masturbate to half-naked 3D characters in games. Do us all a favor, and just die.