I always tile to the floor. It protects the drywall from moisture penetration.

Tile to the floor it will match other side

The baseboard should be continuous and you'd tile up to the baseboard. Unless your tile is thicker than your base, then you could tile all the way and the base would look good butting up to it.

So run the baseboard to the tub and then tile down to the baseboard? Have any photos?

Harder to find than I thought since that spot is so hidden in finished project photos. Here is one. It also depends on your style of baseboard.

Here is one with tile base: https://www.houzz.com/discussions/4613092/thoughts-of-a-tub-that-will-match-white-tiles

Here are better ones.