The most important is to have enough thinset behind the tile to ensure proper adhesion over most of the surface. This can be achieved with both methods (thinset on wall or on tile), as long as the comb trowel's teeth aren't too small.
How much thinset to use depends on the flatness of the wall, a flatter wall (drywall) requires less thinset than something rough like brick. However when applying thinset on the wall with a large trowel, it will automatically put more mortar in the holes and less on the bumps, which is nice. Buttering just the tile doesn't do that, if you butter a tile and stick it on brick it'll just fall off, so it's best to do it only on flat walls.
If you're laying small tiles on drywall, even if you don't need waterproofing, you have to mud the drywall joints before. With large tiles it can be skipped (although that feels cheap) because the tile is much wider than the thinner part of the drywall at the edges, so it will bridge the gap... but with smaller tiles, the one that ends up with its edge close to the edge of the drywall will end up sticking out.
Applying thinset to the wall also forces you to actually look at the wall and feel it under your trowel. If you butter only the tiles, you should skim the whole wall with a trowel first to check for bumps or leftover bits of plaster or mud that stick out and will turn your tile into a see saw. There's always something, and it's much easier to remove when it's not buried in mortar.
To butter small tiles it's easier to put them in a grid on a table with the edges joined and apply the mortar on the whole bunch at once. Otherwise you'll end up buttering both sides. Then swipe a sponge on the edges before putting the tile on the wall, because it's much easier to remove extra mortar when the edges are accessible, rather than later when you only have the width of the joint to work with. Also you need several sponges and buckets, because you will spend a lot of time cleaning mortar off your hands (and everywhere else). Buttering the tiles tends to be a lot messier than just the walls...