Various bits of dialogue change, mainly in being gendered differently. I think there's a couple cases where the master is acknowledged differently due to gender, for example I think sometimes a servant will say gender doesn't matter when it comes to romance. Though I forget if that's specifically triggered by playing as Gudako. Also in this case with Morgan specifically, she calls the player Husband or Wife depending on who you play as. So that's a cute little change.
There's also various different arts in the story for Gudao and Gudako, including how they have differently designed command spells. Mystic Codes / Outfits are designed differently for each master.
Yes they're both the "Chaldea Master" at their core, so the "best master" is largely on if you want to play as Boy/Girl, and various scenarios depending on that factor, art, so fourth. If you want to play as a cute girl that gets the girls, Gudako is obviously the go to choice haha