They are very similar lenses.
I have NON IS of both 2.8 and 4.0
Technically the 2.8 is a better lens,
but I got the 4.0 before I could afford the 2.8

For now
I use the 4.0 when I travel and am going to be outdoors. It is much lighter and easier to travel with.
the 2.8 takes up way too much room.

I use the 2.8 for most everything else.

IQ is really close to equal.
I have amazing shots with both, I really got the 2.8 when I need the extra stop for indoor sports, even then it was not great, so i switched to the 135 2.0 when I had a fixed distance and have some really good photos with that also.

All said I still use the 4.0 because of its smaller size and equal IQ outdoors.