In the NBA, you barely get dinged up from contact. Everything possible foul is called these days. McHale isn't clotheslining Rambis in '16 NBA finals.
In MLB, you have a hard object launched in your direction that is likely to break bones or give you a concussion. There is additional rotator cuff strain that pitchers face due to repetitive motions.
To me, MLB may be less athletic than the NBA, but is more physically demanding due to the higher likelihood of sustaining injuries.