Here is an example
[FEN "8/3k2PB/q7/8/4K3/8/8/8 w - - 0 1"]
One might intuitively say g8=Q is a much better move than g8=R. However, since they both lead to a draw, should we not conclude that g8=Q is as good as g8=R?
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Set aside the particular example you use, and instead assume that we have found some state where two moves are strictly equal under optimal play. Why would you favor one over the other? Let's focus on endgames, since that's the simplest.
The answer, as pointed out by various comments, hinges on the fact that unless you're a masochist playing against a AlphaGo on max settings, you are unlikely to be engaged in optimal play, and thus the candidate moves are not equal in a practical sense. One position might be difficult, in the sense that there is only one drawing ply for you on each move that you have to successfully identify each time, while another is quite easy in that you have many options open to you on a given move. They are both equal under optimal play, but the latter is easier to manage.
Go play around with the Syzygy endgame tables and compare various drawn positions, and in particular the mistakes that are available to the player to move. It's likely that you'll have the sense that some are easy draws, and some are obtuse. For instance, KvK is a clear draw (no possible mistakes), while KQvKQP gives you many opportunities to make a mistake. KQNvKQNP is a tablebase draw in the arrangement, but note that if White plays the Nb5, then it converts to a winning endgame for Black. Seeing this is not at all obvious (at least to me), and other such mistakes are probably lurking. Similarly with different winning and losing endgames.
The strategy here is subtle, and depends in part on your own endgame knowledge and your assessment of your opponent's. Suppose you are playing White and are given the chance to trade into this KQNvKQBP endgame or some other endgame that is also theoretically lost. You know with perfect play it's a loss for White, but there are some opportunities for Black to mess up and for White to steal the win. Do you take the trade? If you're playing against a computer, no, since it has access to the endgame tables. Similarly if you know that your opponent has lots of experience with such positions. If instead you suspect you have more experience, then you might be willing to take the risk to capitalize on your comparative advantage.
Analogy with the opening
I thought that switching focus to the opening might help clarify the thinking here.
The two most common openings in chess are d2d4 and e2e4. I loaded up Stockfish 13 and had it evaluate each ply for a minute. The result is 23 CP for d2d4 and 22 CP for e2e4. Perhaps the former is objectively better, but for all practical purposes they are the same. Suppose you're in the final match of a tournament. Which one do you choose? Obviously, the one you know more about. If somehow you have managed to get to this point without ever playing d2d4, then you probably shouldn't start now, even though it is objectively 'better'.
Similarly, you might avoid going into an opening that your opponent knows more about. Think about how Beth wrestled with whether to play the Sicilian against Borgov in The Queen's Gambit. Maybe if you're a genius, you can get away with playing to your opponent's strengths, but I think most of us would avoid challenging people on their own terf.
Well, according to [Syzygy endgame tablebases](https://syzygy-tables.info/?fen=8/3k2PB/q7/8/4K3/8/8/8_w_-_-_0_1_, g8=R is a loss in 63 plies and g8=Q is a draw. So g8=Q is definitely better.