I find HP5 and FP4 to be perfectly able to manage typical contrasty Southwest light if carefully tested, metered, and developed. HP5 seems to inherently keep shadow detail better, while FP4 seems to inherently keep highlight detail better. Looking at the characteristic curves on the data sheets, you can see why this is. If I need to pull, I prefer HP5. If I need to push, I prefer FP4, as the highlights don't seem to block up as severely as HP5. However, either one is perfectly tweakable if you are willing to put the time into it. Tri-X 320 is a great sheet film as well. I used to use it almost exclusively, but switched to HP5 instead. IMO, the biggest difference between Tri-X 320 and HP5 is that they have different color responses. Tri-X has a very even response across the spectrum, while HP5 is a bit less responsive to the cooler colors.
Since you want a 400 film, I would pick between Tri-X and HP5 (although I would probably be tempted to use FP4 instead if retaining highlight detail was going to be a bigger issue than retaining shadow detail). If you like your pix to seem like they are slightly warm filtered, go for the HP5. If you want a more even color response, go for the Tri-X. Another benefit of this characteristic of Tri-X is that since shadows are cool in tone, they are opened up a little bit compared to HP5. An interesting experiment might be to get a pack of each, put one in one side of the holder and the other in the other side, double your shots onto each side, and develop them together. Either one will give you nice shots, but you will be able to see the slight differences, and decide which one you like better.
I really don't know much about Deltas and T-maxes except that I used them for a while on a suggestion, but ended up disliking the general look. I did not do any testing, but something about them seemed a bit off to me. Personal opinion, of course. I am sure if I took the time to test them, I would see that they have many good uses.