But with the CPU you have, you will get more performance with a more powerful GPU in 99% of the games out.
Again, you missed my point. If the OP sells his parts for say $100 and gets a $250 GPU + i5 system, that will be barely more $ than a $400 GPU especially from HD9xxx series. But at least this system would be balanced. No one is saying he won't benefit from a 7950 in some games but if he intends to get a CPU in the $400 range like 7970GE, it's a total waste of $ for the CPU he has for the games he mentioned. If he doesn't want to upgrade his CPU, then anything above GTX760 is complete waste. You are giving way too much credit to 955-965 and AMD CPUs in general.
For example in Skyrim, 3770K's minimums are 57% higher than 965's:
Phenom II X4's IPC is only at 65nm Kentsfield quad level. 955 isn't going to be faster than Q9550 @ 3.0ghz or Q6600 @ 3.5ghz. Would you recommend anyone buy a 7970/GE to pair with a Q9550 @ 3.0ghz? Not a chance.
http://www.xbitlabs.com/articles/cpu/display/phenom-ii-x4-920-overclocking_8.html#sect0
And just because there are "millions of people" running AMD gaming systems, doesn't mean anything. There are millions of people who think a Ford Mustang is a real sports car and that Dunkin Donuts coffee is actually good. The point is a 955-965 level of CPU is a major bottleneck for cards like GTX680/7970GE and if someone decides to pair this platform with that level of GPUs, they are simply wasting $ on the GPU.
I also paid very close attention to the games the OP wants to upgrade for. He said BF4, which like BF3, is likely going to be one of the most CPU limited games in 64 player matches.
Since you do not believe me, let's look at the facts for BF3 to show you how limiting any X4 CPU is in BF3.
BF3 End Game
HD6870 is getting 52 fps but 955 CPU can only manage 44 fps with 64 people on the map.
Source
Therefore, upgrading the GPU is a waste of time in this level.
BF3 Aftermath
HD7850 is getting 60 fps but 955 CPU can only manage 49 fps with 64 people on the map.
Source
BF3 Armored Kill
HD7870 is getting 48 fps with no AA but the 955 CPU can only manage 45 fps.
Source
What about frame times? Phenom II X4 980 is the
2nd worst CPU for BF3 among modern CPUs tested at TechReport. The GPU they used was XFX Radeon HD 7950.
GTA4 was a notorious CPU pig.
Phenom X4 is a joke for GTA4 compared to even a stock i7 920.
It's interesting how you say that the OP will be fine in 99% of the games out there but the 2 games he specifically is mentioning are most likely going to be in the 1% of the most demanding CPU titles on the PC considering their predecessors were. Ironically, the 965 CPU would be a
major bottleneck in those 2 titles.
I totally understand how people may not be up-to-date with CPU based benchmarks in modern titles but simply stating that Phenom X4 965 is good enough for modern games is misleading. In many modern titles, it's literally 75-100% slower than i7 4770K would be.
If the CPU in question was i5 750-760 that could be overclocked, that would be a different story. Honestly, even when Phenom II X4 965 came out, it was already really far behind the competition in CPU demanding gaming situations. Anecdotal evidence of some $1,300 PC loading games slower than an $800 PC with Phenom II X4 could simply be a matter of the storage sub-system (i.e., 5400-5900 rpm hard drive vs. 7200 rpm). That doesn't actually mean Phenom II X4 was a good gaming CPU. It never was.
In the end, it's the OP's $, not mine. I provided the information so that the OP saves $ or considers selling his system and upgrading the CPU+GPU. Otherwise, he'll continue to become even more CPU limited over time as Skylake is still 2 years away. I don't know how his system even has a hope for playing next gen games with a 965 CPU for that long even with a GPU upgrade.