Promotional copy - any different in sound quality?

Sometimes, but not always, the promo copies come from earlier in the pressing run with an earlier stamper and earlier in the sequence off a given stamper. But there is no guarantee and no consistency about this. I won't pay a premium for a promo copy, but I'm always willing to give one a comparison listen just in case.

The 'promo' really MUST hace a promo (special, different) label to have any value.
Earlier years of LPs had plenty of special label promos.
(for example: Columbia records has a white label instead of the red label..)
A few promo records even come in special vinyl, blue or red.. etc. Or are made from "QuiexII vinyl" from the 1980's on.
The special label promos DO come from the beginning of a pressing, and are more valuable because of being rare. (not because of the sonic superiority, except the "QuiexII" which ARE significantly sonically better.)
When you find a bunch, usually they came from a DJ stash, or a radio station, and are like new.
The later (1970+) promos are mostly just a stamp on the jacket.. which is of no value whatsoever. They are the same records from anywhere in the production run.. and are stamped 'as needed'.

Yes, the promos are much better. I have spent enough time comparing the promo and non-promos of the same. The results are always the same. However, promo copies are often not in good condition.