Well Brad, that's very clever of you, the balls, the oranges, the forest, the tree, wise words indeed.
In other words, when I pick up a roll of HP5, I see that it says, Ilford, HP5, the cassette is white and green, and when I pick up a roll of tri-x, it says Kodak and so forth, so yes, they are different, I confirm.
But HOW, in your experience?
disclaimer: this is all my opinion. I do not have any empirical data to support these claims. Only my own negatives and prints.
First off, I'll admit to loving both of these films dearly. I have used way more Tri-X than HP-5+ however. In fact, untill I tried HP-5 in D-23, I had all but dismissed it as...well, not good for me.
In my experience, HP-5+ really cna be rated at EI-400 (in fresh D-23 or D-76/ID-11), it can easily be rated at EI-800 in ID-68 or Microphen. Tri-X doesn't even come close. I rate Tri-X, somewhat optimistically, at EI-250 in HC-110, D-76/ID-11 and HC-110. It takes a lot of exposure to get Tri-X up off its long toe.
Tri-X looks good in HC-110 - every time. HP-5+ always looks like fecal matter in HC-110 (yeah, I know, this is highly subjective...whatever...see disclaimer above). Both are kinda nice in Accufine but, Tri-X (EI-500 to 640-ish) still does not manage the speed that HP-5+ does (more like EI-800 to 1000). Honestly though , if not for D-23, I wouldn't even bother with HP-5+. In D-23, HP-5 is just magical. I've not found anything quite like it.
The characteristic curves of the two (three if you count both 400TX and 320TXP) films are different. The spectral sensitivities are also subtly different.
As others have already said though, you have to try these things yourself. Nobody can tell you what you like. What fits your style. What works for you. I happen top be a very...ah, shall we say..."carefree" practitioner of the craft. I guess exposures about half the time. I rarely can be bothered to measure the temp of the developer. I re-use a liter of D-23 until it looks so ugly that I cannot stand to look at it anymore - never replenished and really not thinking too much about compensating for number of rolls processed. I like tri-x in HC-110 because it forgives me all these sins. It just works. Same thing with HP-5 and FP-4 in D-23. It just works. I don't really even have to think too much about it anymore. Incidentally, I've tried lots of film/developer combinations. None of them work for me. I keep coming back to my trusty old friends.