Totally unscientific analysis. Checking eBay for "2J collet" brings up 113 results. That includes collets, stops and chucks.
"3J Collet" brings up 260 results.
"16C Collet", 533.
It's been my impression- and of course that's all it is, is an impression- that the 2J, 3J and 22J styles are older. Maybe not truly obsolete yet, but the kind of thing you'd find on old Sjogren chucks and the like.
Whereas 16C is considered more modern- the kind of thing you'll find in power closers, and built into the nose of CNC turning centers.
Personally, it's the kind of thing that if you're just expecting to buy a single set of collets and call it good, any one of them will work- all of them are available new and used, near as I can tell.
But if you're a production shop, and expect to buy odd sizes on a regular basis, or 'emergency' soft collets to machine for special applications, go with the 16C. That seems to have the most current support.
You definitely don't want 22J if you want common. It took me years to assemble a set of 22J collets.
-Took me less than six minutes to assemble a set of 3Js.
Found an L-1 threaded 3J Sjogren on eBay, bid and won. Went to the guy's store to get a total for shipping (I'm in Alaska, of course.) Saw that he had a set of four Hardinge 3J collets, with the auction about to close in literally like a minute and a half. Bid and won, again.
Went back to the guy's store to get a total with shipping, saw there was a second batch of Hardinges about to close. Bid and won those too.
Did that three more times, got a nearly full set of 1/4" to 1-3/4", all, including the chuck, for less than $300.
Doc.