A good machine will do a better job faster and with a whole lot less effort than hand cleaning. I used to hand clean with Aramith - rub on a small dab with a slightly moistened cloth, let it dry and then buff, buff and buff with a micro fiber cloth. In about an hour and with some pretty tired hands I'd get a nicely polished though somewhat slippery set of balls. With my machine (Clean Gleem) I'd get a better result in five or so minutes with hardly any effort - my ball get cleaned much more frequently, less slippery, like new clean and they play consistently every time I'm at my table.
Here's what I know of the available machines (prices may vary)...
Clean Gleem - 8 and 16 ball capacitiy, $399 & $549, unique roller design, solid built to last construction, attractive natural wood finish, made in the USA.
Diamond - 8 and 16 ball capacity, $650 & $850, spinning 'offset' platter design, very heavy solid construction, black wood finish, made in the USA.
Ball Star - 8 ball capacity, $550, spinning platter design, plastic 'crock pot', white, made in Korea(?).
Bludworth - 16 ball capacity, $739, spinning platter design, plastic 'crock pot', black, made in the USA(?).
Generic Chinese - 16 ball capacity, about $150 and up (can you say 'slave labor'?), spinning platter design, mostly white, plastic 'crock pot', made in China. Lots of these machines under various 'brands' have recently appeared on the market (AliBaba, Amazon, Tenu and those sort of places). Caution - your balls may feel like you don't love them.
DIY Bucket Cleaners - many examples on YouTube, revolving platter design (Harbor Fright car buffers and a Home Depot bucket are commonly used), some say they work well plus you did it yourself!
Keep in mind the shipping costs when shopping, some of these big, heavy machines can get quite pricey.
Aramith is the leading cleaner, made and recommended by the company that makes most of the quality ball sets. Said to contain minimal wax. Other cleaners, such as automotive polishes, generally contain mainly wax and silicon - you get a short lived, slippery high polish, not the best for consistent, normally playing balls or for the cloth on your table. Clean Gleem was the first to recommend a 1 tablespoon mixture Aramith shaken up with 1 cup alcohol in a spray bottle. Mist the mixture over your balls in a running machine for a very easy, economical cleaning leaving a like new gleam and consistent, normally playing balls.