There is no evidence to any of the thesises made here.
People say one team was supposedly more "era defining" or "romantic" simply because they vibe more with it. How do you statistically define "era definement" other than subjective factors?
There's evidence. The evidence isn't rigorous? Sure, because there's no systematic (scientific) method of evaluating this.
What Bayern has over Barca:
1) Early European cup success and 1 more CL (although Barca did play in CL finals before Bayern AFAIK. Nevertheless, history remembers winners)
2) Better CL KO record, although part of this is a function of being involved in more tournaments (prior to the rule change) due to being the de facto best team in Germany.
3) Better H2H record if you want to include that
What Barca has over Bayern
1) CL finals wins v Manchester United x 2 and Juventus
2) More impressive trebles
3) More Ballon d'Or Winners and better cast of legends
4) The 09-11 side is considered by football managers (e.g., SAF, Wenger) and players and less importantly, fans, as one of the best club sides of all time. The only names I've seen along with them are Milan 80s, Ajax 70s, RM 50s, and sometimes ZZ's RM.
5) The difference in CLs in 1. But 4 of our titles have come in a tougher, "modern" era while Bayern has 3 in the same. But this is nitpicking and you can ditch this one.
6) 26 League titles v Real Madrid, who is the best club of all time. To me, very impressive.