Is the added cost of the Powermatic lathe a wise investment compared to the Jet 1642? If it is, why?
Only if you think so. It has a bit less over-the bed capacity, but you can always move the head if you want to turn off the end. Betting 98.6% of your turning will be 16 or under.
Bearings don't have to be as heavy, because the swing is less. Upgrades in an easily replaced item are available, but betting you'll not see a need for it, barring abuse, in your lifetime. BTW, be nice to your bearings - use your bandsaw. For a $1300 difference you can get a good one.
Wouldn't know about the difference between 1.5 and 2.0 HP in turning, having only a 1 HP 16" lathe myself. Some people claim there's a need. Depending on your workshop situation, you could be ponying up a bit more to run 240 for the 2HP models of either flavor.
Weight - that perpetual red herring. Bolt on what you want, what you start with is not important, rather what you end up with. Of course, if you use your bandsaw, your low speed and the good geometry of the compulsory stand you should have little problem. You can be nicer to your bearings, too. If you're turning weird shapes, counterweight.
Swing over banjo is at least a pink herring. Unless you're trying to turn in a single mount versus outside/inside, it's meaningless. Though I have to say I like the toolpost on the side versus centered, I could find a way to keep the tool close. Some people give the extra 3/4 of an inch the side post offers back by buying round rests anyway.