Bobby Fischer once said something along the lines of "you gotta give squares to get squares". What he meant is that "getting" stuff always comes with trade-offs. Unless your opponent made a clear mistake, nothing comes for free!
The two openings you quoted are quite seasoned and GMs play them ... that alone tells you that there's no such thing as a "winning advantage" right out of the opening for these two lines.
Space advantages in the center or conserving a center pawn for future use are great things to know ... but you can't just win with that.
If you look at the games of stronger players, you will find them incrementally accumulating advantages and skillfully minimizing the impact of the concessions they themselves make.
When I get a space advantage, the question doesn't immediately become "okay, how do I win now?". It's more likely "okay, how do I maintain this advantage and look for ways to create more weaknesses for him".
As a final note, remember ... there are no such things as silver bullet openings ... they are MERELY a means to get to a playable middlegame with equality as a worst-case and some advantage as best.
(1) ...is trading your opponent's center pawn for your other center pawn (like in the Scotch)?
The implication is that by trading your inactive pawn for his active pawn he will not be able to advance his other center pawn as far as yours, leaving you with slightly more space in the center. From basic chess strategy I understand this is an advantage, but how much of an advantage? If you manage to nurture the advantage through the game will it prove winning, given best play? In other words: is it worth it?
(2) ...is trading your opponent's centre pawn for one of your flank pawns (like in the Old Sicilian)?
The implication is that by trading your flank pawn for his centre pawn, you will be able to later trade a centre pawn for his remaining centre pawn, resulting in you having the only pawn in the center. From basic chess strategy I understand this is an advantage, but how much of an advantage? If you manage to nurture the advantage through the game will it prove winning, given best play? In other words: is it worth it?
__________________________________________________________________________
I'm asking because I'm trying to form an opening reportoire and so far the Scotch seems attractive and the Old Sicilian seems inattractive for the aforementioned reasons. But if both are openings commonly played by both sides, do these advantages even mean anything? To me it seems strange that White would go along with Black's plan in the Old Sicilian if it results in the loss of a center pawn. Likewise, if the Scotch forces Black to give up space in the center, why doesn't every White player use the Scotch?