We should probably start a Bridgewinners poll, but how should it be phrased?
I would think 4S should be the more tightly defined bid. Certainly for suit: I don’t think you’re ever going to bid 4S without a good 6-card suit or some 7-card suit. But if 7 does it need to be better than Qxxxxxx? Probably, since you could always bid 3S and rebid 4S on Qxxxxxx. Not ideal, but nothing else is likely to be idea.
As to 4S being a better hand? I doubt it. I think opener shold almost certainly pass without a fit, and should pass most minimums with a fit. (So 4S is certainly limited, while 3S is not).
BWS says this in general about sequences after a minor suit opening:
After our minor-suit opening and an overcall:
(a) a double is negative through three spades;
(b) two notrump is natural (invitational) and nonforcing (jump or not);
(c) over a simple overcall, a cue-bid shows a raise with game-invitational or greater strength, and a jump cue-bid is a splinter (direct jump-raises are preemptive);
(d) a jump-shift is preemptive.
Among those, (c) is explicitly limited to simple overcalls. (a) can’t be limited to simple overcalls. So conceivably (d) applies, but I doubt it.
Or conceivably this applies, from "Competition After Any Suit One-Bid"
After a jump-overcall: Responder’s jump-shift is fit-showing.
Personally, I doubt either of those applies in MSC.
I could start a Bridgewinners poll with “What does a 4 spade bid show here?”, (allowing people to choose multiple answers) “after 1C - 3D - ? (none vul)”
Choices could be “At least a good 6-card spade suit, or any 7”
“A good spade suit, at least 6 cards”
“Spades; a stronger hand than 3S”
“Spades; but less than an 1S opening bid”
“Spades: but at most a minimum 1S opening bid”
“A club fit, with spades”