This is only my second time building a PC and I don't know which route to go. On one end AMD is cheaper but on another Intel performs better (from what I've been told).  So which build would perform better both cost about the same to buy. 

AMD FX 8350

R7 240 2GB

8GB 1886 DDR3

Or

Intel Core i5-3570K

Geforce GT 610 1GB

8GB 1333 DDR3

Every other part is the same those are the only differences. When I add both up the Intel build is about $15 more which is nothing but would it actually perform better?

Well heres a question, are you building it for gaming? Cause neither of those would really be good for gaming atm but I say go with the intel one either ways. But I wouldn't even bother getting an nvidia 610 cause it won't really help much at all so I would just save the money instead of getting the GPU and just use the integrated intel one and later down the line, save enough money and get a killer GPU for gaming

Do yourself a favor and get a real graphic card... At least a GTX 750 Ti for ~120 €/$

The GT610 is probably even slower than the GPU unit inside the i5-3570K

I recommend you get the i5 over the 8350 as Intel has better single core/ gaming performance. I have a 8350 myself and its decent but if I could go back in time I would have gone for Intel instead. If possible try get a better GPU, both of those models are fairly outdated/weak. Id recommend a Radeon 7870 or GTX 760 minimum especially if you want to game at 900 to 1080p.

Well in my level of experience with pc building I would recomend the AMD build if both cost the same. First of all, that Nvidia GPU is very weak, even when compared to the r7 240 and the i5's iGPU. Then I checked a little both cpus and it seems that the AMD FX 8350 is a little bit more powerful than the i5. But the choice in cpu depends in what you will do with it. I say this because although the 8350 is more powerful as a whole than the i5, the i5's cores are more powerful individually and many games are badly optimsed and/or use few cores (4 at the best). Also the 8350 is easy for overclocking and that stuff (if you are into that).

EDIT: And well the AMD build has faster RAM. although if you want to go a little cheaper you can add more money on the GPU and make the CPU an Athlon x4 860k. I think the FM2+ platform is cheaper than AM3+ (FX) with the benefit that is has better cores and if you aren't planning in getting a killer GPU it won't bottleneck a mid range GPU. Also go for a r7 270x (7870) or some mid level nVidia GPU.

First off, go with the Intel. I went with AMD based on everybody saying it would be just as good. It isn't. I switched to Intel and will never switch back.

Also not seeing why the RAM is only 1333 on the intel. 8 GB of 1600 ram really shouldn't run you very much any more as it has been around quite a while.

As for the graphics card, you've gotta save up for another month or something, because that will be hideous (even for simple games like League of Legends)

If you're going for a decent gaming PC, get an FX 6300 and at least an R7 265 (and better a R7 270 or higher).

if it helps here's my current parts list of the hardware I'm going to be buying in the next few weeks: http://uk.pcpartpicker.com/p/w8dZjX

I already own the GTX 680 (A friend gave me a few weeks back) and another friend donated me his unopened Intel Core i5-3570K both of which have saved me in money, I still need to find a place to buy the SSD though since I want faster boot times and loading for some games.

I would suggest going the Intel route though, I've seen AMD having it's troubles while Intel is expensive they do put out power and stabilization better than AMD can, I'd also suggest a beefier GPU, I'm fine with my 680 for now but I'm either getting a 780ti donated somtime soon but in the end I'm saving for a GTX 980 to carry me through the next 5 years.

Both gpu are really weak. If it's for light gamin go get an a10-7850k instead 

I'm going to assume you are going for a gaming PC. Here is what I recommend:

Intel Core i3 4xxx
Nvidia GTX 960
8 GB 1600MHz or 1333MHz

I would hope costs stay around the same.