Between the GTX 670 and the Radeon 7970 the 7970 gives better performance. With 1 7970 you'd actually be looking at "playable" frame rates. As you can see here,
http://www.tomshardware.com/reviews/radeon-hd-7970-benchmark-tahiti-gcn,3104-7.html
At a resolutions of 5760*1080 (that's 3 monitors at 1080p, highest resolution of monitors you're going to get for $400) the 7970 is getting an average of 30fps on Battlefield 3 Ultra settings no AA. Now 30 fps is way lower than what I'll play at, but that's pretty impressive for such a demanding game. You could always lower your settings to medium and you'd be good to go, and the game still look great at those setting, let alone across 3 monitors.
Now if you really wantecd 2 of one of those cards, well you're not going to get double the quality, but you will have a far higher frame rate possibly making the game really playable. But what you really need to decide now is if you really are going to get 2 cards. This is why,
http://www.tomshardware.com/reviews/geforce-gtx-670-review,3200-16.html
If you see the benchmarks there, 2 GTX 670's outperforms a 2 Radeon 7970's. So if you wanted the best quality you can possible get with those 2 cards, my conclusion would be that if I were to get 1 I'd go with the Radeon 7970, and if I were to get 2, I'd go with a pair of the GTX 670's.
But if this were really up to me I'd do more research and see what technologies I like better. Personally I like the reviews of Nvidias multiscreen setups with 3D capability than I do AMD's. Although, Nvidias 3D requires expensive hardware, where as AMD's you can literally just take some 3D glasses from the movie theater and you're good to go. So I would do definitely do some research to see what you would prefere more on the technology end, because a pair of either cards comes pretty close.
Aslo as a side note, be sure to check reviews before you buy anything. As you can see on some of the cons on this page,
http://www.newegg.com/Product/Product.aspx?Item=N82E16814202008
The Radeon 7970's from Saphire seem to have really large heatsinks that block the second PCIe lane. Atleast that's what most people are saying on the reviews. It would really suck to buy 2 of those to find you can't install them, or that no airflow is getting to one of them. But of course, you could go with a different manufacturer of the 7970 to avoid the problem. Like I said, just check the reviews for quality and the set up you're going for.
Now as far as monitors go. Is that $400 for all 3? or $400 a peice? Here is a very well reviewed monitor that would fit your price range, 3 would be right at $400.
http://www.newegg.com/Product/Product.aspx?Item=N82E16824009420
Those are about the cheapest screens, that have really good reviews, you're going to get at 1080p res and they also have the nice backlit technology, which is very nice.
Anyways, I hope this helps a little on your search for a GPU and Monitor. Don't hesitate to ask any questions!