Conan had an orchestral score based on Carmina Burana by Orf. Conan intentionally minimized the dialog in a manner that worked, this allowed the actors to play to their physical strengths as opposed to looking/sounding out of place. I think that decision is very underrated. Ignoring Arnold Conan also had James Earl Jones and Max von Sydow. Writing credits by Robert E Howard for the character, John Milius, and Oliver Stone.

Compare that to SatS, which had a gimicky 3 bladed sword where you could see the string as it shot the outer blades (how that isn't worse than anything in Conan I don't know). I legit don't know what score it had. Very cheesy dialog. Richard Lynch and Richard Moll I think are the biggest names in the cast. Writing credits by 3 people I've never heard of who, according to IMDB, have a total of 1, 1 and 25 writing credits to their names.

So while you absolutely can and should enjoy whichever one you like more, saying/implying that Conan's popularity is a factor of Arnold's success is just silly.