I recently built a system for myself consisting of:
Samsung 840 SSD (250 GB),
2x4 GB Corsair XMS 1600 RAM,
ASRock H77 Pro4/MVP
a Samsung something-something optical drive
all in my trusty old Antec P150 case
I use the computer to play Skyrim, Crysis 1-2-3, Fallout 3 and New Vegas, Deus Ex, Call of Duty: MWII and (soon, oh, soooooon!) Star Citizen and Elite: Frontier on a single 1920x1080 monitor.
Currently I have my old Asus 5850 GPU to run the show, and it's performing admirably and the computer is very close to being utterly silent... but I want a 7970. So shoot me, but I do.
My question is: will a 3350p bottleneck the 7970? If so, what would be a reasonable pairing for my CPU?
I'm very partial to Gigabyte, I have had a lot of luck with their parts through the years, and I assume i can't really go wrong with a Gigabyte GV-R797TO-3GD - so unless someone can come up with a truly convincing argument, that's what I'll get sometime soon.
I live in Denmark, where prices are... odd compared to what I see at newegg and the like, but I want this system to last me a good while, so I'm not too concerned about price, I just don't want to buy something that's a ridiculous overkill for my processor.
I'm not sure if AMD is doing their "never settle" bundle in your country, but that certainly makes the 7970 more appealing since it includes Crysis 3, Bioshock, and Far Cry 3: Red Dragon.
If it were me, I would go with the 7970 considering the games you are wanting to play.
Having said that, if you'll notice my signature, I have a GTX 670 so that's obviously a good choice as well, although a bit weaker overall. The reason being that I play games that use PhysX. If that weren't the case, I would probably have one of these 7970's right now:
Definitely get the 7970. It will be way better than a 670. You won't bottleneck, and you can do some overclocking with that power supply if you want to. I recommend the sapphire vapor-x cooler. It's fast, quiet, and overclocks well. Your system looks good. Disregard the comment that a 670 beats a 7970. about the same price, better all around except for power draw, which won't be an issue for you.
I managed to install the Vapor-X, but I had to be quite brutal with the HDD cage: I simply used a metal saw to remove a rather large section of the cage, in order to get the card plugged in. The card is maybe 3cm longer than an Antec P150 allows for. No biggie, there's plenty of room for 2 mechanical HDDs left, not that I think I'll ever need more than one, tops, ever again.
The good news is it works just fine, is nearly silent and plays every game I own on maximum settings.