Yes, there is empirical evidence and yes there is an advantage, but the former is fairly limited and the latter is relatively small.
If the spine and the GPP of the X10 and the un-named other arrow are the same, then this is generally the case between the X10 and ACC which have nearly a factor of 3 in the price. The diameter of an ACC however is about 0.8 mm larger for the weaker spines and 1.8 mm larger for stiffer spines. Not a huge difference, but with an average diameter of 5mm for an X10, at the stiffer spines that's almost 40% more surface exposed to the wind.
The advertised weight tolerance and straightness are the same, so James Park's research on the grouping ability of bent arrows isn't any use here except as a reminder that even very bent (0.006", they bounce noticeably when you spin them) aluminium arrows still shoot perfect scores at 18m out of a shooting machine. Since an ACC splinters before it can get that bent, we'd expect the same or smaller groups when shot from a machine. Of course, a human with a bow is a different story, and not something I have enough information to make a guess about currently.
Dr Park does have some empirical (and simulation) results in his paper "Minimizing wind drift of an arrow" (doi 10.1177/1754337111418876 if you can get behind the paywall). He found that for the same spine and gpi, with a 3m/s cross wind in a simulation that have very close results to his compound bow in a shooting machine, an X10 should get 18cm of drift at 70m while an ACC gets 22cm and a X7 gets 26cm. This difference in drift is based on the difference in diameter. In a variable wind we'd expect the X10 to score slightly better if shot by a machine with manual aiming, whether or not the person adjusting the aiming direction is trying to account for changing winds.
So, there is a difference other than hype, but whether it's enough for an average archer, or even an elite one, to benefit from is a different question.