You won't. The number of cores are pretty much irrelevant when it comes to web browsing when you are using such a fast architecture like Haswell. Browsing performance really comes down to more how much RAM your computer has, how much RAM your browser can use, and whether you have Flash enabled or not.
Leaving Flash enabled/ads unblocked when on Firefox for me slows it down to a crawl with me being at best being able to have around 10 of those tabs open before a serious slowdown. With my adblock enabled and Flash needing permission to run, I can really open up as many tabs as I want, given that I don't hit the 3.2GB limit for Firefox because its still only 32-bit.
However, if you have a habit of leaving things open when opening a game or you are planning to run CPU demanding games and video streaming at the same time, you should pass on the i3. My i3-4370 is great, but if I left Youtube or a bunch of tabs open while going to play Skyrim, performance is going to degrade noticeably.