A microwave oven applies microwaves to your sample whereas an ultrasonicator acoustically vibrates your sample at high frequencies.

The microwave oven will cause heating in anything in your sample/solvent that has a magnetic dipole, which is the mechanism by which it heats the water in your food.

I am not a physicist though so I cannot really explain any further.

I have never tried microwaves to stabilize a suspension, but in general, heating causes the colloids/ suspensions to coagulate. Whenever I heated dispersed silica suspensions in organic solvents (indirectly via hot water), particles coagulated. I think microwave will also heat the suspension. The electromagnetic frequency from microwaves is fundamentally different from mechanical vibrations of the sonicator as stated above.

The mechanisms of action are totally different.  Ultrasound creates small (~ 20 um) intensely hot areas (5500K) on collapse of the cavitation bubble.  This imparts a huge amount (acceleration ~ 10E11 g) of localized energy into the system.  This heat is transferred out over a relatively long time scale (minutes) See:

 June 20th, 2013 Ultrasound, cavitation, and the singing kettle  http://tinyurl.com/olueohz

The microwave energy provides vibration (and thus heating) of - OH containing entities (water usually) and provides more general heating but throughout the system and the temperatures (local or otherwise) do not reach the levels attainable in an ultrasound device.  Separation ('dispersion') of particles is thus effected by sonication whereas microwave ovens find their use in speeding up chemical reactions from the rapid heating.  Of course speeding up the reaction is via increasing the collision rates between molecules (and particles) and I the zeta potential in inadequate in an aqueous system then more rapid agglomeration from these increased collisions and sticking.  We've observed this in positively charged CaCO3 particles in suspension where the ultrasound promotes agglomeration rather than dispersion.