So Gen 3 has some weird mechanics (by today's standards, anyway). Whenever both players choose to switch out on the same turn, the order isn't determined by which active Pokemon is faster, but by which player is hosting the battle (the host always switches out first). This is the case in Gen 2 as well, and in Gen 1 it's irrelevant because switches happen instantly on your own screen without waiting for the other player's choice (and their choice will appear to happen first for them too, unless they attacked in which case your switch happens first).
This also has the unfortunate side effect of allowing the host to sacrifice a low HP Pokemon to Spikes damage with zero risk. Since the turn finishes in Singles whenever a Pokemon faints, and the host always switches out first, you guarantee that the other player's attack for that turn will not happen. Even worse, if both players choose to switch out and the host's Pokemon faints to Spikes, the other player's switch does not happen either.
In Gen 2 that kind of situation doesn't happen; the host switches out first, takes Spikes damage, goes to 0 HP, then the other player switches out. Once both new Pokemon are on the field, the host's Pokemon faints. (The turn does end when a Pokemon faints, though, so Player 1 switching and Player 2 attacking will have Player 1 switch and faint and Player 2 doing nothing.)
This also has the unfortunate side effect of allowing the host to sacrifice a low HP Pokemon to Spikes damage with zero risk. Since the turn finishes in Singles whenever a Pokemon faints, and the host always switches out first, you guarantee that the other player's attack for that turn will not happen. Even worse, if both players choose to switch out and the host's Pokemon faints to Spikes, the other player's switch does not happen either.
In Gen 2 that kind of situation doesn't happen; the host switches out first, takes Spikes damage, goes to 0 HP, then the other player switches out. Once both new Pokemon are on the field, the host's Pokemon faints. (The turn does end when a Pokemon faints, though, so Player 1 switching and Player 2 attacking will have Player 1 switch and faint and Player 2 doing nothing.)