I guess it depends on what you are trying to power. For most single GPU solutions a good 850W is enough, and the very high end cards should have around 1000W.
ATX 3s major change is specifying allowances for large power spikes from loads, which older standards didn't define. The difference between 3.0 and 3.1 is a slight modification to the pins on the 12VHPWR connector. The power pins are longer and the connection sense pins are shorter. This is to prevent partially plugged in cables from melting or damaging cards. The spec went from 600W to 675W as well.
No one actually makes a 600W+ GPU yet, and most GPUs even when fiddled with can't use that much power without liquid nitrogen, so it is not much of a difference in practice.
As long as you are careful with your plugs and aren't doing anything too extreme. Nothing wrong with an ATX 3.0 PSU now.