Both can provide smooth live motion when captured, encoded and displayed well. The difference between 50 and 60 frames per second is only one factor; cadence, compression, camera shutter, stream stability and the display’s output timing can matter more than the larger number.
Look for native movement
A stream labelled 60 fps may contain repeated frames from a lower-frame-rate source. That does not create the same motion detail as 60 distinct captured pictures each second. Compare moving players, a fast ball and camera pans rather than relying on a channel name or app category.
Match the display sensibly
A 50 fps source fits a 50Hz or suitable multiple more naturally than a fixed 60Hz output. A 60 fps source suits a corresponding supported mode. Automatic matching can help, but not every application implements it, and mode changes may briefly blank the screen. Use the device’s documented options.
Balance smoothness with cleanliness
Fast sport is difficult to compress, particularly grass, crowds and confetti. A higher-frame-rate feed that is badly compressed can look worse than a cleaner alternative. Watch a whole passage of play and consider sound continuity and stability as well as the apparent smoothness of the ball or scoreboard.