Plastic push-fit vs.compression joints
(this answer has a UK perspective)

As I understand it the main advantage of compression waste fittings is that they are not too fussy about the exact size and material of the pipe. This means they can be used with both the pipe designed for solvent-weld fittings and the pipe designed for pushfit fittings. They also have more wiggle room during assembly which is handy when trying to insert a new fitting into an existing pipe run.

The downside is they are bulkier and cost more than push fit fittings.