holyrage :
no matter how u look at it every card can be Overclocked with a Non reference cooler the GTX670 is a 760 a R9 280 Overclocked outperforms a 760
so i would go with AMD cards regardless 1080P NEEDS THAT 3GB OF RAM so if u can afford going with a R9 280X go with the 280X if u cant go with the R9 280
i would recommend either sapphire or MSI cards also when u get the card just Overclock it and u will outperform any the 760/670
The 670 AMP! uses 680 components, so it's a bit of a hybrid between a 670 with 680 capability, that's why it overclocks so high, and that's also why it's a little faster than a reference 680 in the benchmarks.
However; depending on the price, you can probably find a 960 that will perform just as well. I'd scratch the 760 off that list, no reason to consider it.
It would also be worth stretching your dollar and getting the 970 above them all. It's a significant boost above all three Nvidia cards.