I have a 3770K with a GTX770, and I'm not sure what frames I'm getting but there is no stutter whatsoever at 1080p at the GeForce experience recommended settings in Battlefield 4. Your i5 would work just as well. The mantle support is gonna be interesting to see how it plays out, it looks like it's gonna be quite an improvement, but I'm gonna wait to see how it works in the real world before I jump on my recommendations
If what is being reported is true, and it gets wide acceptance, one of the newer AMD cards may be the way to go. If I had the $400 dollars I spent on my 770 when it came out at the beginning of summer now, and I was looking, the R9 290 would be a serious consideration for me
but as it stands I own a 770 and I love it, it is a great card that plays everything I have at 1080p on top settings with no hiccups at all. The only game I've had some stutter in so far is the newest Assassin's Creed, but I'm pretty sure it is an optimization problem that will be solved either with driver or game updates.