Going against the grain here, but I actually prefer Lunala. It has a flatter, more disc-like shape, and that helps me judge how close to get to the energy rings; Solgaelo's mane gets in the way for me.
I ride Lunala, for game appropriateness. I don't mind riding Solgaleo either, since they both work roughly the same for me.
Solgaleo, even if Lunala looks super cool riding the massive wingspan makes it hard to be to properly aim so I choose Solgaleo as I much prefer being able to do well in there than looking cool.
I ride Solgaleo, I got Sun and Ultra Sun, so it just feels right. Having Solgaleo in both games makes me really attached to it.
I ride Solgaleo because Solgaleo looks so much like Liger Zero from Zoids New Century and it is just awesome anyway.
I prefer to ride Solgaleo. Lunala's giant wingspan can sometimes get in my way and I may either miss/accidentally enter a wormhole.
I stink at the wormhole mini game. Solgaleo is slightly easier for me to use because of the wingspan thing everybody already mentioned.
I thought it would be cool to fly on Lunala, but it actually looks pretty cool for Solgaleo to be running on a trail of light. Aesthetically I guess I don't really have a preference, but like other people have mentioned, Lunala's wings kind of get in the way. It's not just that they make it hard to see/aim, but I think Lunala's hit box is actually pretty small and the wingspan makes it hard to judge if Lunala's actually going to hit something. With Solgaleo, its hit box is pretty much just its entire body. I thought the same thing the first time I saw Solgaleo! It's shiny form kind of looks like Blade Liger too.
I prefer Lunala. Not only does it look really cool, its the reason I got the moon games and not sun. I'm a little tired of the constant lions in Pokémon and I kinda see Solgaleo as just another lion. But the main reason I choose Lunala is because I hate the idea of some creature running through a portal with no clear defining ground and I'd prefer something that flies in this situation.
Constant lions? I can only think of like, three. Granted, one of them WAS just one generation ago. Personally, I like riding Solgaleo because of the wingspan thing so many people mentioned already. But with the Pokémon themselves, Solgaleo just barely beats out Lunala for me.
There's the Shinx line and the Litleo line in addition to Solgaleo. For bats there's the Zubat line and Woobat line in addition to Lunala. Unless I'm forgetting any, I think there's the same number for both lions and bats. I guess you could count Absol, maybe, since it's a sphynx, and maybe Entei since it's based on a komainu, which started off being represented as a Lion, then became more canine-like (adding to the constant struggle of what to call the legendary "dogs")
I guess I'm just bored of lions over bats. Probably because lions are more popular in main stream media than bats so I'm a little tired of lions across all of media. Guess that has nothing to do with the amount of lion Pokémon.
Solgaleo, aside from just being my favorite of the two, feels a bit easier to steer around hazards and wormholes that you don't want to enter. I've tried using Lunala a few times, but I'm in the same boat as everyone else who has issues with its wingspan making it harder to judge where you're going.
Lunala because it has a unique design of some moon bat compared to Solgaleo who is just another lion Pokémon.