Is the IQ a big different between 70-200mm f4L IS and 70-200mm f2.8 II?

I don't have the 2.8 II, I have the non IS 2.8. I have used the f4 IS and it is a fine lens.

I thought long and hard about my normal subject matter, shooting style and determined that the 70-200 f2.8 non IS would suit my needs better than the 70-200 f4 IS. You may come to a different conclusion.

I've been happy with my decision so far.