While I've heard amps with just about every tube type, here's what tubes I can comment on in context of hearing all on the same system -- mine -- but of course in different amps:
300B -- SET, PSET, PP
845 -- SET, PSET, PP
45 -- SET
KT88 -- SEP, PSEP, PP
EL34 -- SEP, PSEP, PP
EL84 -- SEP, PSEP, PP
211 -- SET
2a3 -- SET
PX25 -- SET
Amp design, circuit topology, quality of transformers and related circuit parts, and even the tubes you select all have profound effects on amps built with these tubes. But there are some characteristics that seem attached to the tube type itself, which shine through differences in implementation.
45: Penetrating intimacy in the midrange, soft top, deep natural bass. However, even on 101db/w/m Zu Definitions, the dynamic limits of a 45 amp in SET configuration are so acute that it is not practical in American listening spaces. The first watt may be critical, but your average SPL doesn't have to be all that high at 12' distance for you to run smack into the dynamic compression (and distortion) of 2 watts more often than you like. Music with muted dynamic range, however, can be beautiful through this tube. I wanted to be bowled over by the Yamamoto but the dynamic limits couldn't take the 45 all the way.
2a3: Similar limitations as the 45. A little less neutrality than the 45, more romantic. Lush.
300B: A big 7 or 8 watts makes a difference in maintaining dynamic clarity. Magical midrange richness is a real trait, easily identified. Rising harmonic distortion in the bass region generates characteristic bloat that can be designed out at a substantial price. Treble "spray" is lush and exciting but with some tubes, like mesh plates, is on the far side of real.
845: Big, meaty tone. Much more bass discipline than 300B and top end extension is more neutral. Midrange is unmistakably triode and rich, but gives up some of the 300B's delicate articulation. Dynamic slam however walks all over the 300B, even when that tube is used in PSET configuration for similar power. The quality that most sticks out with respect to the 845 is its sheer drive. On some speakers, this tube is unbeatable, except perhaps by the Godzilla T-1610. The 845A, 845B, 845C, 845M, KR 845 and the vintage RCA or United are all different enough to overwhelm these distinctions.
211: Similar to 845 but a little drier.
EL34: Warm, round sound. No one ever regretted listening to an EL34 amp.
EL84: Sweet, open, driven, with surprising bass discipline in SEP topology. Amaze yourself and embarrass many high-buck SET amps with an Almarro A205mkII.
KT88: Take-charge tube with speed, transparency, tone. Strong tube that can give you up to a solid 15w/ch in SEP configuration, with a "whiter" more objective sound than most triodes, and very fine tonal and detail balance. The Acoustic Masterpiece M101, for example, can take a lot of triode amps to school.
PX25: Best bass I've heard from a triode tube in SE. This is the "objective" triode, stripped of the 300B's up-front emotion, with a few extra watts over a 45 to put the vice-grips and some kick to a speaker cone. Lacks the emotional romance of the 300B, but midrange is open and fluid, just a tad tonally anemic. The top end dispenses with the 300B's spray. The Audion and Art Audio PX25 amps are the smoothest segue into low-power SET for someone coming from Push-Pull.
I can say more about each tube, but is this a start for you? For reference, my systems actively use 300B, 845, and KT88 amps today.
Phil