2 cents again...
1) If the grip becomes a limiting factor, and I need to really train hard, I will use straps, as I want to get everything from the legs, hips, back and not let the grip get in the way.
2) If it is pulling as in deads, and I am going over 3-5 reps. I use straps so I pull without torquing my torso using a mixed grip for higfher reps. I always use straps for stuff like RDL's, x8's x10's+ and shrugs, maybe even bent rows.
3) I also have noticed, that if my dead goes up #25, my grip, even though I was using straps, will follow suit most times and be fine for low reps and max weights.
4) Why not use both? I mean why limit your choices?
5) Gripping muscles seem to recover pretty quickly (2 days) so I always have room for grip work ie: static holds or some squeezing and one arm pickups.
6) I use chalk quite a bit too.
7) If strapping, wear them more down on the back of the hand then wrap, don't wear them on the wrists.