27.5 is more nimble, agile, and swift when whipping around tight corners. They are more playful. Watch pro riders whip their bikes mid air n stuff. Drift the rear tires around berms n whatnot. 27.5 more suited for action sports sorta of extreme riding. They are easy to manuever in narrow technical trails.
29" more stable, they roll and truck over bumps and rough terrain better. The bigger tire isn't robbed of momentum as much by bumps, thus, making it easy to get up and over obstacles and keeps you going better. They absorb bumps better that would really jar you up on smaller tires, assuming same amount of suspension and tire width. 29ers smoother ride overall, but are harder to make sharp turns. Whereas the 27.5 is better are narrow twisty trails. And 26" is king at whipping sharp turns.
29er best for wide open south west US: Calif, Ari, Nevada, Utah, all those deserty regions
27.5 best for northwest, northeast forests. Oregon, Washington, Canada, etc.
26 is used in Downhill cuz smaller wheels are stronger. And 180-200mm suspension plays the role in dampening bumps.
Some bikes are being made to fit 29 and 27.5 Plus. Plus meaning very wide tires in the 2.6-3" range. Some trails are best on 29, others you might appreciate the 27.5 more.