How would the Sun's activity be different if it didn't rotate differentially? Why?

"Yes, the Sun does rotate. We can observed this by observing sunspots.
All sunspots move across the face of the Sun. This motion is part of
the general rotation of the Sun on its axis. Observations also
indicate that the Sun does not rotate as a solid body, but it spins
differentially. That means that it rotates faster at the equator of
the Sun and slower at its poles. (The gas giants Jupiter and Saturn
also have differential rotation.) The movements of the sunspots
indicate that the Sun rotates once every 27 days at the equator, but
only once in 31 days at the poles."

http://imagine.gsfc.nasa.gov/docs/ask_astro/answers/970108a.html
"Rotation of the Sun" By Padi Boyd, Imagine the Universe!

One would expect sunspots to rotate at the same periodicity regardless
of location if the Sun did not rotate differentially.  This would be
because the Sun would be rotating as a solid body.

Sincerely,

Wonko

This service is wonderful!