You've got some ears!The only difference in "tone" I can say I've ever noticed between rectifiers is more sag from a lower power rect., or say if I have 2 5U4's,if one is weaker than the other causing a bit more sag.A rectifier is not in the signal chain and should have little if any effect on the tone.Like I said,if one is somewhat weaker,there may be a noticeable difference in response,but it will hardly be noticeable to most people.
I hear the challenge in your question, and, to clarify, I did not speak about "tone" differences. I use that "t" word for amplitude differences in frequency bands: more/less bass, low-mids, upper-mids, etc. That is not the kind of differences I am referring to.
We may be discussing the same thing - what you call "sag" may be what I'm noticing between different rectifiers. But what I hear is not dependent upon "weak" or "strong" electronic capacity - a weak testing Tung-Sol 5U4GB is closer in character to a strong Tung-Sol than it is to a weak or strong Sylvania 5U4GB.
For the Ken-Rad 5U4Gs, for instance, I note more clarity/definition (or, perhaps, less compression) than the RCA 5U4Gs I've tried. Weaker, or stronger, the sonic character remains. Some prefer the RCA because of this character, some prefer the Ken-Rad - it is a matter of taste. 5U4G and 5U4GB tube types are spec-ed a little differently, with GB having slightly less voltage drop, yet I've noted much more compressed murkiness from stronger Sylvania 5U4GB.
Maybe I've got great hearing (it tests very well). Or maybe I just care to pay closer attention to this phenomenon, which most of the world couldn't really care less about.