1♠-2♥-3♥-3♠-3NT-4♣-? (opponents passing throughout)
Opener has agreed hearts. Responder cues spades, yielding a serious 3NT from Opener. Responder now cues 4♣. What is the difference between Opener bidding 4♦ and 4♥?
On the one hand, you could interpret things along these lines. Opener's 4♦ sounds like a cuebid. If he needed a diamond control, he would not cuebid 4♦. Hence, 4♥ essentially asks for a diamond control. 4♦, in contrast, is a sort of "Last Train" bid but definitely shows a diamond control, seeking generally "more stuff."
On the other hand, you could interpret things another way. Opener's 4♦ sounds like and should be "Last Train." When control of a suit has not been showed yet, Last Train implies a lack of that missing-suit control. Hence, 4♦ "asks" for a diamond control. By process of elimination, then, 4♥ becomes a "general stuff" invite, showing a diamond control. The bypass of what is essentially an "asking" bid, or a "denial" cue, shows that which would otherwise be requested/denied.
The risk is that you interpret this auction under the first reasonable approach but partner interprets this auction under the second reasonable approach. Better to agree.
Personally, I see little merit to going one way or the other. I see a small technical advantage to the second line, in that I might want to "ask" about a diamond control even if I have one, and only the 4♦ as asking approach allows that. I also, for perhaps strange reasons, feel that the second theoretically is more consistent, not with cuebidding generally but with Last Train theory specifically. Hence, I lean toward option two. But, reasonable minds can differ.
Again, this is probably a very good discussion point. Save yourself from having a silly argument when it comes up.