Look at how musicians stand the test of time. There are musicians from the first century that we still talk about! And everyone can name 10 composers. Do you think everyone could name 10 athletes from 1900 and earlier?
The only problem with that comparison is the fact that professional musicians have been around a lot longer than professional athletes. Even today, amateur athletes (aside from college and high school) are not well known. Professional athletes didn't really come about until around the turn of the 20th century (1900), though professional baseball players did come about in the late 1800's. Long story short, it's the professional athlete that gets the bulk of the attention even today, and there really weren't that many prior to 1900, so that's why it's much easier to name musicians from a long time ago, and athletes not so much......however, there are several professional athletes from way back then who are just as well known today, as they were 75-100 years ago.....so, with regards to elite professional athletes, they have shown the ability to survive the test of time.
That being said, I'd go with being the greatest athlete in the world and play professional baseball because of longevity, it not being as taxing on the body over the long haul and later in life, and most importantly because of the money. Hell, even mediocre baseball players can pull in $10+ million a year......and if I'm the greatest and in the elite class, I could easily command $25-$30 million a season & build from there as my career progresses. Of course I'd have to play for the Yankees, Red Sox, or Phillies these days because they are probably the only ones who could afford me. Ha ha ha! Many musicians unfortunately only receive pennies of every dollar that they earn through their music.....atheletes pretty much keep the lion's share of what they earn.