I haven't used the 150-500mm, so my answer will be based on sample images i've seen here and other sites for that lens.
I've owned the 100-300mm f/4 for a couple of years. I use it for sports and birding/wildlife. the last couple of days I've been using it fo birds, shooting out of my blind , with and without a tc.
Shooting 100-300mm without the tc, the 150-500mm will not come close. The IQ of the 100-300 is just better in terms of sharpness , contrast and about everything else. From reports of the AF on the 150-500, the 100-300 will smoke it in this regard also.
The 100-300 handdles a 1.4 tc very well. It does take a little hit, but not much. Since the 150-500 is 6.3 at 420, stop the 100-300 down to 6.3 and it picks up whatever it lost, except for the AF speed. It doesn't take that big of hit on the AF, and I mainly can tell the difference when birding.
So between these 2 lens I would go with the 100-300mm f/4. But if your going to use it mainly for birding, I would take a hard look at the Canon 400mm 5.6 prime lens.