need advice: i3 or i5?

hi all, long story short. i'm planning a major upgrade for my old rig, which runs on - CPU: Intel C2D E7200 2.53Ghz; GPU: Nvidia GTX 560Ti. 

With a tight budget, I'm aiming for an ivy bridge processor, either a i3 3220 or i5 3330, but i will keep my current GPU. I will not overclock.

the rig is mostly for gaming, ideally with the power to comfortably run all modern games on hd with details on high (not max) 

So my questions are:

1. considering budget constraints (no hard cap, but the less the better), which of the two processors is a better investment for the purpose i described?

2. how big is the difference between these two processors when coupled with my 560Ti?

3. True or false? very few games actually take full advantage of quad core, hence i3 more than suffices.

Looking forward to your input and suggestions. Thanks.   

but seeing that i5 3330 (2.7Ghz) is actually a low-end quad core, is the investment worth it? Or perhaps i should spend just a little bit more for 3470? 

If it means sticking up another gas station to get the money, go with the cheaper one. Tom's Gaming CPU Hierarchy Chart ( http://www.tomshardware.com/reviews/gaming-cpu-review-overclock,3106-5.html ) shows them only one tier apart, which is supposed to mean that the performance difference for gaming will not be great. Few games use four cores. That said, cough up the extra sixty bucks. You will be glad you did. A small but noticeable performance difference is worth it, and it might be enough to bump your settings to high in the more demanding titles. Some games do use four cores, like Crysis, and when you try to play the ones that do you will have one foot in a bucket with the dual-core. Anyway, you want to be able to hold your head high down at the comic book store, don't you? It's a quad-core world.Blistrax

Don't buy a dual core in 2013 if you want to do more than internet browsing and office work.