Your hand is just an orbital buffer in really really really slow motion. So the difference in results is directly proportional to the amount of labor/time you put into the hand-polishing, versus what the machine can accomplish at a far more rapid pace.

So, if your question is a matter of results, factored along with TIME and (manual energy) invested, you can't beat the machine.

However, there are limits to what the machine can do. You can't get into tight areas, or sharply/deeply contoured areas with your average orbital. So you're always going to have to "finish it out" in many areas around the car by hand, after you've done the more expansive surfaces by machine. Also, I don't like taking the machine toward the edge of panels where I'd meet up with a molding, or matte surface, or gap, etc.etc..., potentially altering (permanently-glossing) the matte or flat original finish, as the aggressive polishing rate of the machine can be too aggressive for your belt-line moldings (at the base of side windows), your 1/4 window moldings, any badges and scripts, etc... Plus, they typically get wax and polish down into crevices and gaps and under moldings/weatherstrips, which sticks out like a sore thumb once everything dries, and is a bear to get cleaned out and cleaned up. That's counterproductive, saving time by using a machine, but using it sloppily such that you've got tons of time wasted in after-detail and cleanup.

So polishing or waxing your car is kinda like painting a room. Use the machine for the large and expansive areas, where it fits and where the pad makes even contact with the paint. Then, "jamb out" and "edge out" the rest of the car you missed with the machine by hand. Then buff off.