(This answer contains mild spoilers for the game.)
Short Answer: Nope.
Longer Answer: Although the twins do have minor cosmetic differences between them, it ultimately makes no difference who you pick.
Aether, the male twin, has a color scheme that matches the first gliding wings you get. Lumine looks better with the Frostbearing Tree wings, I think.
There are slight differences between their fighting styles, as in the video below, but the effect is the same.
Aether has a slightly faster movement speed, Lumine had a slightly faster attacking speed. Lumine also used her feet more during her animations, which makes her look more graceful, and uses her left hand to cast her elemental skill while Aether uses his right. Both twins use their right hands for their sword.
Genshin Impact – Main Characters / Characters – TV Tropes
Genshin Impact Main Character Index: Main Characters Mondstadt: Knights of Favonius | Four Winds | Mondstadt Others Liyue: Liyue Qixing | Adepti | Liyue Others Inazuma: Inazuma Antagonistic Factions: Fatui (Fatui Harbingers) | Abyss Order | …
Storywise, Aether is the canon protagonist. He’s the one shown most often in trailers, art, and other official materials, and some of the in-game voice lines assume you’re Aether, even if you play as Lumine. That doesn’t happen very often though.
However, it really makes no difference as to who you pick. Most players ditch the Traveller in favor of other characters from the gacha relatively quickly. You also get to date everyone in the Hangout Events and story quests no matter who you pick.
There is speculation that the Twins’ fighting style is “incomplete” without the other twin, because they’re used to fighting together like the opening cutscenes with the Unknown God. Hence the lack of a third passive talent for the Traveller — some are guessing that it will only be revealed after the Twins meet again.
So TL;DR — there’s no real difference in the Twins beyond appearance and animations. Aether is the canon protagonist but the game will not punish you for being Lumine.