I'm a heavy HP5 400+ user and it is constantly in my fridge or on my desk or in my cameras.
I shoot it consistently at 800ASA and do a 1-stop push in development. I also push it to 1600ASA and do a 2-stop push when developing. I develop with Ilford DDX but I think my lab uses Kodak Developer (Tmax Dev I think?).
In both cases, I find I like the look. I like the extra contrast associated with pushing the film and, in some situations, even the grain. It suits me and the way I like my photographs.
Strangely, the grain doesn't tend to be all that distracting to me in most cases as I'm normally pushing to 1600ASA when there is dim lighting (I don't like HP5 at 1600ASA and pushed two stops in development in bright day light though... in this case, I look for a more smoother look... but really, it's all preference).
HP5 is quite a flexible film and I really like it's "pushed" qualities. I have yet to try it at 3200... that would be interesting.
I actually also like TMAX but more when it's pushed 1-stop and rated at 800ASA (same methodology as when shooting HP5). It's a little different in some ways but I find it fits my art
It's a bit "cleaner" than HP5 in my own opinion. Results may vary for you.
I think the best way to think about the different films is the difference in "tones" (someone correct me here if I speak blasphemy!) and look. I like the look I get from HP5 400+ and TMAX400 ... when shot at 800ASA and pushed +1 stop in development. The "tonality" with Delta, and even Tri-X for that matter, appears different to me. Not particular to my liking... but sometimes it is
One other thing to consider is the lenses. Certain lenses have a look that affects the final image when used with different films. I'm presuming you're using one lens to check these films out but just thought I'd put that out there.