This is an important questions to ask yourself, especially if you're upgrading on a small budget or, like me, a stroke-inducingly microscopic one. Other upgrades notwithstanding, I've been following a pattern for the last few years when buying video cards; every two years I grab a new high-end card (so I usually replace a really old graphics card). Not the tip-top of the scale (although I would if I could, and I recommend it, if it doesn't crack your financial security in half), just bellow. But that doesn't mean that the card won't be expensive; the last one I bought cost me half as much as my rent, and I live in LA.
Buying a higher-end model over a lower-end one pretty much ensures that you will be able to run, on high graphics settings, any game that comes out within the next two years (providing you have good enough CPU and RAM). At least this has been my experience. Now, let's talk brands.
First off; if you are currently running an on-board Intel graphics chip, then I have some words of wisdom for you, "it's never too late to repent of past mistakes". There is no upgrading to Intel, only upgrading from.
Second on the list; The Eternal Battle: Nvidia vs. AMD(formerly ATI) For me, I buy Nvidia for one reason, and one reason only, namely: PhysX. Otherwise, the capability of the cards is, generally, the same, and the price is pretty much identical (most powerful: $999 and second most: $499, but after that it varies a little more). Also, Nvidia currently supports OpenGL 4.3, but AMD only supports 4.2 (if you care about that sort of thing). For certain games, though, the PhysX chip makes all the difference. You get absolutely beautiful water, particles, and cloth, leaving the regular GPU part of the cart to worry about everything else. Thing is, not all games use PhysX, most don't.
Not here for gaming upgrade advice? Then that last paragraph, or so, didn't mean diddly to you, but you should still get rid of your old graphics card. If you're, what say, doing something with some kind of 2D or 3D Graphics software (from Adobe Photoshop to Flash to Autodesk 3Ds Max)and you don't want your computer to chug, then you have two options available to you. 1: Buy the beefiest cart you can find, and never worry again. Or 2: Buy smart; buy for your project.
Are you making a Flash based cartoon? You probably won't need anything $300, if that. Are you tinkering in 3Ds Max, but hope to make fantastic 3D short films later on? Something between $350 and $400 should do the trick. Are you building a 3 hour long stroll through a photo-realistic forest, indistinguishable from the real thing, where you could even count the hairs on the head of an errant monkey, which, by the way, you could swear was a living, breathing, creature? (what is wrong with you?) Then go out and buy two or three of the most expensive card you can find. I hope your motherboard is SLI/CrossfireX compatible, or that someone bothers telling you to be a little less eccentric.
If you want to know which is truly better (Nvidia or AMD), you won't find that information here. There are a hundred reasons each side can think of for why theirs is better, but neither side can be more right than the other. Honestly, if Nvidia opened up PhysX, so that any graphics card could use it, I would probably switch to AMD. Why? Because I buy their processors, but we can talk about that later.