I don't think it's a case of one being universally worse than the other. It all depends on how you use your computer.
A computer with 2GB of RAM and an integrated graphics card can theoretically run games better than the same computer with a 1GB dedicated RAM card, because under ideal conditions it'd be able to dedicate almost all 2GB of its own memory to graphics, whereas the dedicated card has a maximum of 1GB, no matter what the rest of the computer's memory is doing.
However, if you have background programs running (which most computers do), then large chunks of integrated RAM can be lost in the middle of a game if a program of higher importance decides it wants to do something while you're playing (antivirus programs are particular bastards for this).
It all comes down to how well you can manage your computer's memory for it. If left to its own devices it'll often result in unreliable / worse graphics if it uses an integrated system. Integrated systems are potentially better, but are so much of a pain to set up to their full potential that in 99% of cases a dedicated one is more useful IRL.
.... Is using "IRL" to describe computer graphics an oxymoron? idk.