I've used both but I prefer a keyed chuck. In general the keyless chuck works fine but in some instances I need to get the chuck tighter and this is where the keyed chuck is better.
Agree. I have a keyless chuck on my drill press and also in my cordless drill - they work OK, but I just feel more comfortable with a keyed chuck.
That said, the one thing to be aware of when using keyed chucks is to always remove the key before starting to drill. If you leave the key in the chuck, it can be flung out and into your face when you start up the lathe. And in a lathe application, there is the related issue where to put the key so that you can always find it when you need it. A woodturning workstation can get pretty cluttered - - - My solution was to turn a wooden handle that I glued the short metal handle on the key into, and then I made a holder that is attached to the end of the lathe bench that holds that handle. The handle makes the key much larger so that it's more difficult for it to get lost, while also providing the potential for applying more torque when tightening the chuck (for those who care about such things), and having a special place to put the key means that its less likely to get lost in shavings.
I bought the MT1 PSI chuck when I had my first lathe, and as Edgar said, it was threaded to receive a 1/4x20 drawbar. When I moved up to an MT2 lathe, I bought a replacement arbor from Little Machine Shop that allowed me to upgrade the chuck to MT2. The replacement arbor is threaded for a 3/8x16 draw bar which is what I normally use today. Lathes generally don't come with drawbars (they should), but its ridiculously easy to make one - just get a length of the appropriate all-thread rod from the hardware store, and then turn a knob with an embedded nut to go on the end. That knob can be as simple or fancy as you wish. I made mine in two pieces that fit together with a mortise and tenon arrangement, and embedded a t-nut at the point where they join.