So I did a thing... kind of a Hoya v Yau analysis. The other day, I heard someone refer to Hoya as "objectively inferior to Yau" on 4x4, citing inefficiency. I sort of thought that way of thinking was done with by now, so I wanted to test it. The only objective test for efficiency that I could think to easily measure was movecount. So...
I did a Mo12 of movecounts and broke it down by F4C, Hoya Cross, L2C, with Total. This leaves off at L8E, where we merge with Yau. I tried to do what I thought I'd do in an actual solve, not taking too much time to influence better cases. The Results:
F4C: 25, 17, 23, 23, 24, 24, 20, 21, 23, 29, 20, 24 = 22.75
Hoya Cross: 21, 28, 27, 31, 27, 41, 30, 24, 28, 28, 33, 33 = 29.25
L2C: 10, 9, 10, 6, 11, 11, 10, 8, 11, 8, 5, 9 = 9.00
Total: 56, 55, 60, 60, 61, 76, 60, 53, 62, 65, 58, 66 = 61.00
I went to the Reconstruction Database to start comparing. I used World Records set using Yau, figuring those were representative of potential. Singles usually have lucky cases, for instance Feliks' WR single of 21.54 (when combining moves like U' U' into just U2) took 49 STM moves to get to L8E. So I looked at Averages instead. 3 were available:
Mats Valk at German Open 2012: 33.57.
Moves to L8E: 55, 59, 54, 62, 56. Mo5 was 57.2.
Sebastian Weyer at Aachen Summer Open 2012: 30.81.
Moves to L8E: 58, 48, 50, 53, 55. Mo5 was 52.8
Sebastian again at Frankfurt Cube Days 2014. 28.15.
Moves to L8E: 65, 55, 62, 62, 58. Mo5 was 60.4.
So... what I gather from this is that while Yau could be more efficient than Hoya, the gap is not nearly as wide as people make it out to be. Sebastian's 28.15 average especially showed this.
Obviously there's a lot more to each method than just movecount. There are different movesets being used at different steps. There's different uses of rotations. There's differences in recognition, lookahead, algs, just to name a few. So this is not the definitive way to judge the methods. It is food for thought, though.
Edit: the person who I quoted at the beginning has since retracted the word "objectively" after reading this post :-D