it's tough to say, honestly. especially for me, who's always on the sidelines of fandom groups. i can mostly judge the popularity of a certain ship or ship-name by the type of art/fiction that i see on the web. more precisely - by the way people themselves tag their creative works. and, to be fair, the tag doesn't always tell you the whole picture. when characters are as complex as these two, their relationship can't be simple either. so i can see lots of scenarios where elements of both shuada and adashu dynamics can organically coexist. and these are pretty neat scenarios, in my opinion.

but yeah, just from the tags, i'd say that i've personally spotted more shuada than adashu (or even # adashuada/shuadashu, the unfortunately rare tags) in the past few years. i definetely didn't make any sort of statistical research and don't stand by this claim, haha.
at the same time, if you look at the fandom's collective creativity over the years.. who knows, maybe adashu would win? i definitely remember seeing 'adashu' as a prevalent tag on pixiv in ~2017, for instance. and most of the ao3 "heritage" from early 2010s is "adasou" as well. so i guess the two would balance each other out, time-wise.

thanks for asking and glad if i'm providing at least any sort of entertainment with my thoughts here :'>