I asked the same questions 2 years ago...
I got the I3 3220 ivy bridge...
and
an A10 I built for my dad...
My problem wasn't money... was I am on a solar set up, but, I also wanted to play games at low power...
Anyway, the A10 doesn't really or isn't really that fast for modern games...
The i3 with a dedicated video card, in my case an a 777 AMD, yes the 777 card isn't that fast but it's also fast enough to play modern games at well, medium graphics levels without sucking down a huge amount of power.
So.... For me..... the i3 with a dedicated GPU was the winner choice.
But, on the other hand if I only had 160 bucks to spend........ I would have gone with the AMD APU setup. It is way faster than the i3 onboard crap GPU... Upgrade path is bullshit, since.... I usually build a new system every 2-3 year anyway. If I'm gonna upgrade, I'm gonna see what better chips, might as well, just buy a new system and sell off the parts for whatever you can get.
So.... yeah, you'd be better off with a AMD if you have a tight budget. Another thing that is BS, the intel fan boy's will tell you the power on a a10 is 95 watts (true) and the power for i3 suck down 35 watts... But add in that 100-200 watt video card... there goes that crapshoot.
This all being said, I am extremely happy with my I3 and 777 card setup, I've played farcry 3 and 4 at moderate levels and my didn't have to run the generator to do it! Solar is the way to go! The 777 card is an amazing card that sips power. But will pull the watts in heavy gaming.
Anyway... go with the AMD ... If you can't afford a GPU card...
https://www.youtube.com/watch?v=fmHCCOJBdE0
Go with i3 if you can spare an extra 100 bucks for a GPU card.
https://www.youtube.com/watch?v=6b5hxmibmao