My quad-core computer is not faster than my single-core computer at browsing the web. Likewise, a quad-core phone will not be faster than a dual-core phone or even a single-core phone if you don't have apps that need that power.
I have a quad core pc and a single core. I'd say the quad beats the single in every way. But.. I guess we will have to wait and see what happens in the phone world. I'm not a big web user with my phone.
I would agree that the quad beats the single, but I would also contend that a lot of PC games are designed to run on at least dual-cores, if not quad-cores, whereas many Android games are designed for single-cores. So the performance difference between a single- and a quad-core phone, while it may sometimes be evident, is not especially important at the moment. Not saying that won't change in the future, because I'm sure it will. For the moment, however, there isn't much of a functional difference between single-, dual-, and even quad-core Android phones. The software is just not to the point of needing that kind of hardware.