Ultrasonic homogeneizers creates strong oscilating pressure gradients across small distances in a dispersion. In consequence, the dispersed phase vibrates back and forth in all directions (spherical waves), eventually breaking. Vorterx mixers generates strong velocity gradients across small distances, associated to eddies of various sizes. In consequence, the dispersed phase is subjected to viscous shear, eventually breaking. Regarding ads and cons, you will end up looking for price, operational cost and maintenance. I guess, vortex mixers are much cheaper. However, it depends also on the problem scale (bench, pilot, industrial).
Micro and nano particles tend to aggregate in aqueous media, particularly when zeta potential is low. Thus, the particles may lose functions. Thus, hemogenizing is needed before use of the suspension. But I do not think vortex is strong enough to break such aggregates. Use ultrasound.
The working principle of the two are totally different. The first one, the ultrasonic homogenizer generates the ultrasonic (40kHz generally) high pressure waves right into the sample resulting into cavitation. The other one is the vortex mixture which basically vibrates the full container with liquid. The frequency may relatively be smaller than ultrasonic method. The more effective and advantageous is obviously the ultrasonic. In this you can control frequency, intensity etc.