This is a big question. Some of the dx12 cards would benefit from it others would not. Some games might look/feel better but that is it. Most of the times when a new api comes around tends to be more taxing to the gpus since new graphical technologies are being applied. So the overall graphics are better but at a certain cost.
Except some more expensive scenarios (like 2 gpu on non sli config or with a really good cpu/gpu combo) i wouldn't expect to see any positive difference between 11 and 12. If anything,, budget cards might have to struggle more. In your case i wouldn't worry about. Almost all the titles should play as usual.Hope that helps