unsure which processor will be better for me

For gaming?

I would save money on the Intel build, by stepping down to a Core i5-3570K and perhaps some slower RAM (1866 is fine).

Or wait for Haswell. Less than a month away now.

1600Mhz memory that has good, fast timings is actually just fine, faster RAM (higher bus speed) wont make any difference that you will be able to tell by sitting in front of the screen. You will notice that as you raise the bus rate the ram runs at, the latencies get longer, or higher.
You don't need more bus width once you get to 1333-1600 range, you actually have all the bus speed you can really use, you want to search for memory that has low latency.

I'd stick with the 3770 build, however, if you opt for the cpu down grade I'd get the 8350 build. it's already been proven that is better for multi thread applications and games.

It's generally a bit better than the i5 for multithreaded applications, but not for games.

Added: I see others have chimed in while I was writing this took some Breaks - LOL
This adds supports jitpublisher Comments which I fully agree with. End Added

Totally agree with Sakkura, unless Multitasking is a priority, go with the i5. For gaming very little diff between the i5 and the i7. This could change down stream if Games start coding for use of more than 2 or 4 cores.
On Ram, I'd go one step more than Sakkura on Ram and recommend DDR3-1600 even with no cost difference.
1) Above DDR3-1600 voids Intel's CPU warrantee. NOT an issue when you start OCing as that in itself voids the warrantee unless you purchase the OC warrantee (if they still offer it. it was like $20 to $25 for my i5-2500K. Ram Spec for SB/IB: Both 1.425 -> 1.575 Volts, SB is DDR3-1333 raised to DDR3-1600 For IB.
How valid is this?? as I have DDR3-1600 CL7 @ 1.600 Volts for My i5-2500 and have been running for close to 2 years with no problem. However For Your IB the 2133 is two steps above spec.

2) Performance: http://www.anandtech.com/show/4503/sandy-bridge-memory-scaling-choosing-the-best-ddr3/6
Somewhat Dated, but still pretty much valid. For games very little gain from 1600->2133. There are a few apps that take advantage of increased BW, gaming is just not one of them. Same-Same for CL ratings.

Reason Freq of DDR3 above Spec is not the best Idea UNLESS you have a specific application that will take advantage of it.
.. For SB/IB the memory controller is now on-die. As Freq goes up, Impedance goes down, current goes up and so does power (heat). This is primarily the result of Xc , Impedance or apparent Resistance (Xc = 1/2πF) So If F goes up, Xc goes down. As resistance goes down, current goes Up (I=E/R). Then Power = Voltage x Current (or I^2*R) - Text box does not like sub or super script - LOL) Much more complex is the effect on Phase shift on signal.
Bottom line here is if you have a App that has a NOTICABLE performance gain using the Higher clock ram, go for it; OTHERWISE, Stick with the Spec, DDR3-1600 CL8.

My vote is the IB system. Please do not jump down my throat. This is not the AMD vs Intel CPU, It's about chipsets, and 3rd party hardware and software. Very unfortunate fact of life. Intels support chipsets are generally better, with more frequent updates. primarily a result of loss of personnel at AMD and RMD budget. As For 3rd party development, If you were developing a piece of Hardware or software, with AMD @ 20% and Intel at 80% (Just approximate %s), who would you tailor for optimum performance? Hopefully they would be the same, but NOT always the case, ie SATA III SSD.

you should look a little harder at that I think.

Apparently (I'm not a gamer) but based on: http://www.anandtech.com/bench/Product/697?vs=701
the i5-3570K beets the FX8350 in:
Dragon Age Origins
Dawn of War II
WOW
StarCraft.
Only Games they listed
Also for i7-3770, just change the i5 in the pull down menue

Yes the Fx8350 beats the i5 is some application (Kills the i5 in 7-Zip Test), Ties in others or too close to ever notice in real life) and loses in some. Unless Your Utilization is weighted heavy toward the Apps where the FX8350 wins then the best choice in my opinion is the i5-3750, or if those apps are that important then go the i7 route. Basically the FX8350 only is a viable choice is when the cost difference between the 3770 and FX8350 is a deal breaker.

Added: If you do change the i5->i7 you will see the i7 does beat the i5 in the four listed games, Just not enough to warrant the cost differential

Tom's had a similar test, which did shows some minor performance gains with faster memory. There are diminishing returns though.

Yup, correct, However:
1) BENCHMark diff:
.. 1600 -> 2133 = A whooping 3%
.. 1600 -> 1866 = 2%
.. 1866 -> 2133 = 1%
Outside of a benchmark (a very few select applications) does anybody think they will see the diff in real life day-2-day usage. An definitely does not compensate for working the CPU harder.

2) Two devices that I find synthetic Benchmarks useless are Ram and Sata III SSDs. The only Valid way to compare is using real application - Reason Reviewers do Not do this often as it is hard to show a real difference.

... For SSDs as an example
Using AS SSD (ATTO is NOT a good Benchmark for SSDs).
My Crucial M4, and Samsung 830's score mid 700s. My Samsung 840 Pro is a Whooping 1100 (on series 7 MBs they score around 1200). Bet if I lined up the three systems, you would not be able to tell which is which. I'd probably lose as the 840 pro is 2->3 sec faster at boot - BUT no diff noticed once windows has loaded - eyeballs just not calibrated to see a few millisec difference - LOL

"It definitely makes sense to buy a DDR3-1600 kit, and even DDR3-1866 nudges performance forward a little. Stepping up to DDR3-2133 really doesn’t do anything though."

Quoted from the article at Tom's referring to their general final analysis of memory performance for an i7, 3770 Ivy-Bridge CPU based machine after all is said and done. If you look at the entire article, it seems that software using compression/decompression features like winRAR can make some use of faster memory as far as benchmarking programs can show, though once again these are quite small and likely completely unseen in real work use.

I stand firmly beside my suggestion of buying good, quality, low latency 1600mhz memory for any modern gaming build and you will have no need of wondering if your memory is performing as well as it should.