I'll explain in a very simple language.
Theoritically, a CPU has to be fast enough to feed the insturctions to the GPU.
Small hypothetical examples.
Example #1
You pair HD 6570 with a Pentium 4. You get 40 FPS in a game. Then you pair HD 6850 with a Pentium 4. You still get ~40 FPS in a game.
This was an example of "CPU bottleneck" - in which CPU was not fast enough to run the game and feed instructions to the GPU. So if using a Pentium 4, then getting anything above HD 6570 will give you zero benefit in games.
Example #2
Guy X purchased Phenom II X4 965 BE (Rs. 7500), a motherboard (Rs. 6000) and HD 6970 (Rs. 21000). Total cost = Rs. 34,500.
Guy Y purchased Core i7-930 (Rs. 13000), a motherboard (Rs. 10000) and HD 6850 (Rs. 11000). Total cost = Rs. 34,000.
Core i7-930 is the faster processor than Phenom II X4 965 BE. But Guy X's computer will be faster than Guy Y's computer in games.
Reason? Guy X has a much much faster GPU. And Phenom II X4 965 BE might be quite a bit slower than Core i7-930, but it is in no way a "bottleneck" and still powerful enough to feed a HD 6970.
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Example #3
One more example. X4 965 + HD 6970 vs i7-930 + HD 6970 when playing games at a very low resolution of 1024x768.
So, in this case we are playing on a very low resolution. Pairing both the CPUs with the same GPU.
You'll expect i7-930 to win in this case because it is the faster CPU afterall. In low resolutions, you are not "working" up the GPU by much. GPU load will be low and CPU speed will affect the winner.
Less resolution = CPU bound. But no one games at these resolutions anymore. 1920x1080 performance is what everyone should look at.
Example #4
X4 965 + HD 6970 vs i7-930 + HD 6970 when playing games at 1920x1080. You could say this is a high resolution.
In this case, don't expect the gap between both the configs to be much. Both will perform similarly. May be the i7-930 config will win, but not by much.
Both processors are avoiding the bottleneck and 1920x1080 resolution is more GPU intensive. GPU load will be high.
More resolution = GPU bound.
Example #5 - multi-GPU and multiple displays.
a)
Let's use HD 6990 + HD 6970 "Trifire"....that's three GPUs. Resolution = 5760x1080. Three 1920x1080 displays. Processors we will use are FX-8150 vs i5-2500k.
Resolution is very very high - both CPU and GPU will get worked. In this case you'll see that i5-2500k will win if the game is CPU intensive. Because FX-8150 is the slower processor.
Multi-monitor resolutoin gaming = the type of game will make a huge difference here. GPU intensive obviously, but if the game is CPU intensive, CPU performance will make a difference.
b)
HardOCP had tested GTX 580 2-way SLI and 3-way SLI on i5-2500k and FX-8150 respectively. Their result:
HardOCP said:
If you are running dual-GPUs, such as 2-way SLI, this again will be dependent on the game, but also the resolution. There are several games that show some major differences between the CPUs, even with 2-way SLI, such as ARMA 2, Crysis Warhead and Civilization V. On the other hand there are games that do not, DiRT 3, Dragon Age 2, Metro 2033.
What is very clear though, is that with 3-way SLI, performance was continually better, and noticeable to a large degree, with the Intel 2500K CPU. It seemed to us that the AMD FX-8150 CPU was holding back the performance of 3-way SLI.
AMD FX-8150 Multi-GPU Gameplay Performance Review
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Now we have games. Few games are single-threaded and few are multi-threaded. Majority of games now use 2 threads at the moment. But from 2010 we are seeing that most games are utilising 4 threads.
Starcraft 2 - for example. Single-threaded and CPU intensive. Core i3-2100 (2 cores/4 threads) will win against Phenom II X4 965 BE (4 cores/4 threads) regardless of the GPU you use. SC2 is very CPU intensive - almost like a low-resolution game scaled up.
GTA IV - very CPU intensive game. The more cores you add, the better it is. X4 965 BE being a quad-core will win against i3-2100 (dual hyperthreaded cores). Faster GPU made no difference for this game. All it needed was 4 cores and overclocking to run properly when it was released. Nothing less.
Resident Evil 5 - can make use of upto 8 threads. FX-8150 (8 cores) might have a chance against i5-2500k (4 cores) here.
Battlefield 3 - an example of dual-threaded GPU intensive game. No matter how many cores and which processor you throw at it (Phenom II, FX or Sandy Bridge) - it used only 2 threads and performed equally. The GPU solely defined the performance in this game.
Civilization V - multi-threaded, very CPU intensive and very GPU intensive.
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Nutshell: Gaming performance = mixing and matching of many things. There are aberrations to what I wrote above - but it is still a fair gist overall to the best of my knowledge.
Regarding your Phenom II X2 550 BE. It alongwith Core 2 Duo E74xx/E85xx is fine for gaming at least for the time being. 550 BE overclocks nicely as well. If you feel it is slow, overclock it. It will not be fine from next year or so. Games are starting to utilise 4 threads now. Pretty much the reason why Athlon II X4 gets more recommendation than this in TDF.