I can’t speak to the AXS mountain bike rear derailleurs, but my Force AXS eTap RD is quite silent and has a less high pitched sound than Di2 Ultegra. Whether you prefer one of the other is IMHO like a discussion over exhaust noise. Personally, I don’t care either way.
I think what you are experiencing are slightly “chunkier” shifts of SRAM group sets with mountain bike cassettes in general. (I have tried Force 1 and XX1 11-speed with 10-42 cassettes.) So I don’t think this has anything to do with the groupset being electronic or not, and is largely a matter of taste. I have yet to try a 12-speed Shimano mountain bike groupset, so I don’t know how they compare. My 9-year old Shimano XT drive train shifts more smoothly now than it did initially. I just attribute that to years and years of usage. I can tell, because the rear up shifter works both ways. I almost exclusively use my thumb, so the index finger direction is “almost new”.
Still, I think the advantages of SRAM eTap groupsets, especially the fact that there exists Rival eTap AXS now, is a problem. The cumulative advantage is IMHO substantial and if I were agnostic in terms of hood shape and button layout, I see clear advantages with going SRAM eTap AXS. Just the 10-36 cassette alone is a huge boon, especially for more average riders, riders who want to go 1x or if you want a quiver killer bike. Shimano has nothing like it in its drop bar groupset range.