I'm using an Asus R9 270/AMD Phenom 1100t 6 core and I want to upgrade both. But I was looking to get a new GPU first. I was looking at the GTX 750ti, but the GTX950 and R9 380 is about the same price. What would be the best budget GPU that can play with decent FPS at 1080p?

It looks like you are looking for something in the $100-$200 range. At the high end of that the R9 380 is excellent for 1080p gaming and you should be able to play many titles on high or max settings at 1080p with a decent framerate. The 950 still offers good performance at 1080p but you may need to turn some settings down. However, I would not upgrade to a 750 Ti from your current R9 270, as I don't see the value in that.

The 390 is your best bet in that range:

http://gpuboss.com/gpus/...90-vs-GeForce-GTX-750-Ti