I can fit either into my budget with no struggle i just want to know which is better for gaming and multitasking, please attempt to keep in mind cost effectiveness because if the 1055t is only slightly better than the 960t it would be silly. I already have an AMD mobo, so no I's please.
I'd say either get a Black edition CPU such as 1090TBE or a 975BE and overclock it. The 1055T is fine but has a locked multiplier. You can still OC it of course, just easier to have an unlocked multiplier ^_^. I would only go with the 8120 if you spend a lot of time encoding and use encoders that can use 8 threads, but not much benefit for gaming over the 1100T or 1090T even when you consider overclocking.
A 10 would be an overclocked to within an inch of its life 5GHz i7-2700k, but interestingly, even a 4 on this scale is enough for most games and should handle anything really, unless you're into super high res multi monitor gaming. As the basis of a 1080p gaming rig, I'd recommend that 960 and add a modest third party CPU cooler to give it a bit more grunt. If it unlocks to 6 cores, then that's a bonus and will take it from a humble 4 to a juicy 6.
This scale was sidesniped from cinebench multithreaded benchmark scores so it's a little skewed towards the more threads being used the better but however you look at it, the order of the processors is about right in terms of general performance too.