Compare and contrast the two different types of mechanical waves?

There are longitudinal and transverse.  Both types of mechanical waves require a medium, transport energy, and have defined wavelengths, frequencies, and speeds.
Differences are that transverse waves oscillate along a direction perpendicular to the direction of travel (like shaking a rope up and down).  Longitudinal waves like oscillations along a spring and sound waves, oscillate back and forth along the direction of travel.