What is the main difference between the acoustic and electromagnetic waves?
Reciprocity, particularly in Air acoustics.  If you are down wind from from an acoustic source like an animal and you hear it, you are less likely to be heard by it.  The same effect is true with currents in underwater acoustics but to a lesser extent because sound velocity is relatively greater than fluid velocity. 

The variation of sound speed tends to be more important in simulations. There are specializations of the wave equation, actually more typically the Helmholtz equation to account for things like $c(z)$, depth dependence. 

Acoustic waves do not have polarization, but do have vector particle velocity. 

At the other extreme, the speed of light can not be exceeded while the speed of sound isn’t a universal constant.

The Friis equation is not used in acoustics.  Isotropic lossless propagation in acoustics is usually inverse R squared. The term “path loss” have different conventions. The Friis equation implicitly includes the aperture of the receiver, so for isotropic lossless propagation, the path loss is proportional to frequency.  Radio engineers often (stubbornly) claim that low frequencies propagate further because of the Friis equation. Lower frequencies do often propagate further but typically it is because refraction is related to wave length, so in terrestrial point to point communications, the curve of the earth, scatter by objects like houses, penetration into buildings, and mode coupling between the earth’s surface and ionosphere favor low frequency propagation.  High frequencies tend toward line of sight.  Friis isn’t why.

In acoustics, performance is typically ambient noise limited while in radio,  the limit is usually related to the antenna temperature. When an array is moving through water, flow noise can exceed ambient noise. The calculation of array gain differs accordingly.

Acoustic waves are often encountered in combination with sheer waves.  There are also slow waves in EM propagation but sheer wave propagation is essential in seismology.

In biological systems, first principle bulk properties like the Young’s modulus of living lung tissue tend to be avoided because they are very complex to model and directly measure, particularly if you don’t want to kill the subject.

There is also a distinct area of research relating acoustics to perception.  Humans (and animals) are better at localizing sounds than classic array theory predicts.