I think Madonna irritated more people in the world than Mariah, but people just got used to it and just accepted who she was. In terms of their place in pop culture, I think Madonna is respected more - she's after all the Queen of pop. As a performer, Madonna is probably more respected despite her limitations. In terms of being a musician and a vocalist, Mariah takes the cake here obviously.
Mariah. Madonna got by with controversy and was a genius businesswoman. When people think of the musically talented of that time, they think of Michael Jackson, Prince, Whitney, Mariah and Janet. People credit Madonna with a lot of what she didn't or wasn't the first to do.
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Anyway
G0d obvs. Most people either don't care about Madonna or thinks she's an attention starved hag who made a few good songs. Contrary to what forum geighs would have you believe, the average person is not kissing her feet or calling her some otherworldly music visionary.
Whereas with G0d most people either don't care or thinks she's a past her prime, washed up (one of a kind) vocalist.
Madonna is not actually that respected by the GP at large. I hear a lot of negative things about her like 'dress your age' etc if she's ever brought up in conversation. Also a lot of older generations do not like her overt sexuality and classically trained musicians consider her music to be trash.
That being said Mariah is not that respected either as her behavior post-Mottola years is considered diva and absurd.