Not with the Equalizer specifically, but on 9mm M&P 2.0 full size comp vs. standard I found there to be no difference in felt recoil, muzzle rise or split times. I ran both (set up virtually identically) on a shot timer, back to back on the same day and the difference between the comp and standard was less than the standard deviation in the two data sets. For reference, my splits averaged ~.18 sec.
My opinion is that most of the factory "comp" guns do not have a true "compensator"... they have ports without a blast plate/expansion chamber because the hole in the front of the slide needs to be big enough for the barrel, not just the projectile. As a result, most of the gas just goes out the front because there is no restriction to re-direct it in a direction that reduces recoil. I did notice that on the chronograph, the Comp version was 30-40fps on average slower than the standard gun, because the last ~3/4" of barrel is free bore and larger diameter.