Foil kites have always drifted better for a long time now, long before wave kites were a concept.
Two things come to mind though what is drift and what is better? Drift is broken into two areas. One is the ability of the kite to stay flying with no tension in the lines. The other is a kite that maintains line tension when others would lose it, as in it tracks downwind with you.
For surfing no line tension is amazing. The kite does not exist and so a complete surf feel is achieved and things like proper cut backs and direction changes are possible. Foil kites are more capable at this but harder to use and not all foil kites are equal. Bigger foil kites are better at this, certain designs too and generally lower aspect as well. The skills to manage a foil kite to drift and when it goes wrong are quite a bit, but it can seem easy when you get it right and is magical.
Kites that maintain line tension are horrible, but that's my opinion because I like no tension and kites like that won't do it or do it easy. Foil kites generally don't maintain line tension naturally, but some models do it a bit. You can however make a foil kite do it. A foil kite can relatively easily be made to position any where in the window.
Also a distinction between the styles of surf kiting and wave kiting needs to be made. Surf kiting uses the kite to catch waves but generally not ride them. In reality you can't use a kite to ride a wave because you are then riding the kite and not the wave. Which then becomes wave kiting which is using the kite to ride on or near the wave. You will regularly see "wave" kiters do turns completely assisted by the kite, like on the flat in front of the wave. They also use it to power into slashing turns at the top of the wave, where the biggest spray is to be achieved. I think because this is a difficult feat with out a kite it makes them feel satisfied
Personally though I think style is a preference. I do like wave style sometimes, but I prefer surf feel, getting barrels and oh airstyle strapless