AMD doesn't have anything comparable.
What games really care about (most of the time) is the speed of your graphic card. Get a good graphic card.
After that what games really care about is called single thread performance of your cpu. The higher the single thread performance the higher the games perform.
After single thread performance what games care about is multi thread performance, but they only care about performance per thread up to four threads. There are very little games out there that care about more than 4 threads (there are a couple though). This is because when a game designer designs a game they have to divide up the work the game is performing. It is very easy to put all the work on 1 or 2 threads, and almost impossible to put the work on anything more than 4 threads due to how games work underneath it all. Some games can use 5 or 6 threads but if those games use 5 or 6 threads they are barely using thread 5 and 6 so there is little benefit from a quad core vs a hex core vs an octocore with equal single thread performance.
This is a limited website with a limited benchmark but it gives you a good idea on cpu performance. Look at the single thread rating for it is more important for games.
http://www.passmark.com/index.html
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If you get double the number you get double the performance, notice how you are barely getting any single threaded increase with the intel cpus even though in the end we are going to compare cpus which have a price ratio of 5:1. Notice though you get a 3:1 multi thread ratio when you spend 5 times as much but only a 23% increase in single thread performance for spending 5 times as much.
$70 Intel Pentium G3240 @ 3.10GHz , 2 Cores, 2 Threads
1851 - Single Thread Rating
3498 - Multi Thread Rating. 3498 / 2 Threads is about 1749 per thread with only 2 threads capable
$115 Intel Core I3 4130 @ 3.40Ghz, 2 Cores, 4 Threads
1976 - Single Thread Rating
4824 - Multi Thread Rating, 4824 / 4 Thread is about 1206 per thread with 4 threads capable. How hyperthreading works (making a dual core do 4 threads) is that for the first two threads you get about 1976 in performance for the first thread, 1976 in performance for the second thread if you are only using 2 threads. 1976*2=3952. But if the software needs 3 or 4 threads it can better utilize parts of the cpu resources between the two cores so it can strech that 3952 score and make it 4824. So for thread 1, 2, 3 and 4 the performance is somewhere between 1206 and 1976. Allocating resources to the threads that need the most resources and less resources to the threads that need less resources. Your cpu is a very good delegator.
$220 Intel Core i5-4670K @ 3.40GHz turbo to 3.80 Ghz, 4 Cores, 4 Threads
2228 - Single Thread Rating
7758 - Multi Thread Rating, 7758 / 4 Thread is about 1939 per thread with 4 threads. Now notice this 1939 per thread is less than 2228 single thread. This is due to turbo (which the i3 and pentiums lack). If only using 1 thread you can hit the max of 2228 but if you are using 2 threads it is in between those numbers and if you are using 3 or 4 threads it is 1939 per thread. This is probably the best value out there for a gaming cpu.
$330 Intel Core i7-4770k @ 3.50Ghz turbo up to 3.90 Ghz, 4 Cores, 8 Threads
2281 - Single Thread Rating
10313 - Multi Thread Rating, 10313 / 8 Thread is about 1289 per thread with 8 threads. You only get the benefit of the i7 versus the i5 if you are using threads 5, 6, 7, and 8. That and a small speed boost for the cpu is 100 mhz faster which is about 3% faster on threads 1, 2, 3, and 4. Thus if you are only using threads 1, 2, 3, and 4 your multi thread rating is about 8000. You are only gaining that extra 2000 if you are using threads 5, 6, 7, and 8. Due to games barely using threads 5, 6, 7, and 8 you get barely any extra cpu performance.
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Now the best AMD cpu out there under $300 is called the AMD FX 8350 and it goes for about $190. It is an 8 "core" with 8 threads and no hyperthreading (it has something similar to hyperthreading, but for simplicity sake just ignore it)
$190 AMD FX 8350
1510 - Single Thread Rating (notice this number is lower than the pentium)
9040 - Multi Thread Rating. 9040 / 8 is about 1130 per thread. So for only 1 thread you score 1510, but if you using threads 2 to 4 your score will decrease for you can't turbo as high, it decreases even more if you are using threads 5 to 8 to the minimum of 1130 per thread.
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Your old cpu
Intel Core i7 950
1316 - Single Thread Rating
5647 - Multi Thread Rating 5647 / 8 threads is about 705 per thread.
That said 1212 multi thread rating per thread if you are only using 4 threads or less. Due to having 4 actual cores and the remaining 705 is only achieved if you split up the resources due to using 8 threads at one time so in some tasks your 4 year old i7 is as fast as the best amd (see above)
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So in sum AMD has nothing that compares to intel gaming wise as the intel i5 4670k or the intel i7 4770k. In some tasks that can take advantage of 8 threads (such as video conversion since this can use all 8 threads at once) the AMD FX 8350 is better than the i5 4670k and almost as good as the intel i7 4770k while being a $140 dollars cheaper.
That said the AMD FX8350 and the i3, i5, and i7 are all not slow, but I would not upgrade at all unless I was getting the i5 4670k or the i7 4770k.
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Now of course since you are not upgrading now but in a month the newer devil canyon processors will probably be better. Then again you may get a good deal on the older i5 and i7s because the new devil canyons are coming out.