There's more disadvantages to a 6j than there are advantages. But when you need or like those advantages they're invaluable. As said the main advantage of a 6-jaw chuck is the ability to hold thin wall work with much less deformation so it depends on the work you do. I got into machining cause I used to mod flashlights heavily. I would need to hold flashlight parts like bodies, tailcaps, heads, reflectors, etc. I remember the first time I tried to hold a small plastic reflector, they kept fly out of the 3j & I destroyed 5 of them before giving up. Some of the custom reflectors were quite pricey & some were hard to get. Had to resort to making custom collets/jigs to hold certain parts with a 3j. That got to be a PITA quick.
They say a 6j is a second op chuck & an adjustable 6j can be an alternative to collets. Not in the sense for safety for close up work (the jaws) but cause you can quickly chuck up a semi finished part pretty accurately & quickly. I have a ER40 chuck for may lathe but I pretty much never use it. It takes too long, my 6j is much quicker & pretty damn accurate. Of course a 5C setup with a collet closer would be quickest which I don't have. Collets also are not an advantage for me cause I don't always work with nominal size parts. I only use collets when I'm really scared for my knuckles. More jaws equals more pain, trust me I know!
I find with the 6j I can chuck up shorter parts more accurately & quicker than a 3j, with more jaws it much easier to chuck up a short part straight (axially) without having to use a pusher tool like a ball bearing mounted on a bar or indicate. With that said, a 4j should hold thin wall parts better than a 3j. But yes & no, 4j independent is the most popular but chances are you tend to deform a part more because each jaw is independent & you just naturally put more pressure on a part with each jaw. Now with a 4j scroll or combo chuck yes, they seem to be less popular though.
Some say a 6j holds better & some say they don't. More jaws doesn't necessarily mean more/better grip. In my experience it goes both ways. 6j will hold thin wall & smaller diameters better but with larger more solid work you can get slippage. I use a 3j or 4j when I really need to grab a hold of something tight, because they'll dig into the part better. With more jaws there's more surface area holding the part so a 6j does not dig in well, the force through the scroll is transferred through more jaws. But that's another advantage for me. I'm anal, I hate leaving jaw marks on parts & in many cases I can't as I have to chuck on a finished area.
I've had work slip in my 6j before, most of the time I can just crank down on it harder & be fine. I no longer do that cause it's not worth the added wear on it. That's when I use a 3j.
Some say a 6j does not grip well if the stock is not perfectly round. This is true in theory but it hasn't been a problem for me. I buy stock from a large metal supplier that i'm lucky to have locally, I rarely use stock that I scrounged somewhere. So pretty much all the stock I buy is cold rolled/extruded/ground, they come well rounded & are not beat up. Of course not perfectly round but again I've never had a problem.
Even though I don't work on flashlights much anymore these days, my 6j is still my primary chuck. I use it 80% of the time, followed by my 4j indie, then my 3j, & again collets have not been useful to me with the type of stuff I work on. Being so used to the 6j I can't live without it. When I got my new Bison 3j Set-Tru, I tried to use it as my primary chuck, I just couldn't, I found myself switching back to my 6j alot. I guess I'm just too used to using my 6j.
There's more disadvantages but my post is way too long already, plus I'm a 6j fan boy so I'll leave those "absurd negative disadvantages" for others to post. Haha
And my disclaimer: I'm just a hobby dude & not a machinist by trade. These are just my experiences & opinions, I may have no idea what I'm even talking about.
