I can tell you one thing - tiling to the sides of the tub is a !
Tile the deck and drop the tub in, make sure you caulk it well so the water won't get under, a little sealer and you're good to go. It also takes a lot less precision and will give you a nice line around the tub.
If you put the tub in first and then cut tile to it, especially if the tub is round, you will never get it to fit perfectly.
Now if there is no tub deck, thus you're just tiling walls down to the tub, then you have to install tub first and tile later.