My vote's for the Stones.
Though, the Meghan Trainor video following does have a whopping 126,357,432 hits on YouTube...
REALLY?! Are people that "proud to be fat" that this makes them feel triumphant?
I suppose you could argue that the Stones song is misogynist and mean...But when I -- a young woman, a gay young woman -- first heard it on a classic rock station in the late '70s, I immediately interpreted it as a brilliant, open-ended (non-gender-specific) "fuck you" song to whoever had once spurned you.
With "All About That Bass"... Repeating the idea "I'm big and fat but I'm sexy" dozens of times doesn't make it so. Meghan Trainor jumping around in frou-frou pastels doesn't look "sexy" at all. Not only because she's overweight, but because she also looks like a generic mall girl jumping around in frou-frou pastels. Not to mention that overtly proclaiming that you're attractive/sexy pretty much indicates that you're not---that it takes promotion and hype rather than any actual innate reaction from viewers. This song's beat is sassy, but the idea isn't at all "sassy" to me; it's just forced, received PC-ness and, thus, a bit embarrassing to see the subsequent hit count: "I'm told that something is proper to like, and so I must like it."
When it comes to this Stones song, though... You're not supposed to (according to today's prep-school-raised rich kids now working for northeastern media outlets, for instance, and/or middle-school teachers) like it better, but... you do. Because it's 100% more psychologically honest, however disturbing the actual real sentiment.