A drain cable — a snake — is a steel coil driven down the pipe by a motor. It works by force: it breaks up whatever is in the way and opens a channel for water to move through. It is fast, it is inexpensive, and for a single obstruction it is exactly the right tool.
What a cable does not do is clean the pipe. If a four-inch line has an inch of hardened grease coating the wall, the cable bores a hole through the middle of it and the water runs again. The grease is still there, the diameter is still reduced, and the line will close back up on roughly the same schedule it did before.
Hydro jetting attacks the wall instead of the center. Water at several thousand PSI comes out of a nozzle angled backward, which both propels the hose up the line and strips grease, soap scale, sludge and root hair off the pipe as it is pulled back. When it is done properly the line is at full diameter, not merely open.
The practical rule: if a line has backed up once, cable it. If it has backed up more than once in a year, or if it serves a commercial kitchen, jetting is the honest answer. Grease and root mass do not respond to a cable for long.
One caution that matters more than the choice itself. Jetting a pipe that is already cracked, offset or collapsing can make the damage worse, so the line should be cameraed first. If the pipe is sound, jet it and camera it again afterward so you can see what you paid for. If it isn't, that footage just saved you from spending money on a line that needs replacing instead.