I've tried all of them out lately, including a MIJ (which I own).
The MIM PJ is more traditional and versatile than many others, but has less of a unique character - which could be good or bad. It is well built, but feels rougher around the edges to me than some of the others. The P pickup is pretty nice, but the J pickup is somewhat weak. They sound good together, but I wouldn't be soloing the J much in stock form.
The Vintera I played had a more substantial neck and felt better built than the PJ, and the pickup goes into a more traditional mustang vibe - which is sort of p-bassy, with darker lower mids, big bottom end, but a different presence in the upper mids. Being lower winds on the pickup, it has less "beef" to the sound, and more stringy high end. This one would probably give the most "clank" of all of them, but setup, strings, and tone control.
The JMJ has an even bigger neck, feels more broken in, and the pickup has even more mids, but isn't as stringy sounding as the Vintera. As it comes with flat wound strings, it also has a very different vibe than the vintera. Seeing as the JMJ and Vintera are almost the same price, this is for sure the one I'd pick between those two, as I prefer the bigger neck, broken in feel, better pickup, better tuners and flats.
The American performer is in many ways a better built bass than the others. The neck is noticably higher quality. While I haven't loved them new in store, I have a friend who owns one, and after only a few weeks of playing, his clearly has the nicest neck of all of them. The quality of the neck, frets, etc mean this one really has a more focussed sound with the least "clank" of any (except for maybe the JMJ). The finger board edges are rolled in a way that makes all of the others seem very squared off. The mustang pickup is very nicely voiced - not as aggressive a top end as more vintage style mustangs, and in contrast to my MIJ (with a nordstrom), more mid range focus and less exaggerated bottom and top end. Very balanced, but also a little less exciting than some mustang pickups. The J pickup on it, however, is outstanding and it really opens up new possibilities on the mustang. Together, it gives a lot of versatility. My only downside is that the mustang pickup, itself, isn't as exciting as the pickup in the JMJ or the nordstrom I have in my mij.
And while it isn't on your list - the MIJ mustangs are quite good too. Slimmer neck than the vintera, JMJ or American performer, which would might love or hate. Gloss neck too, which, again, some people love, some don't. I personally love it! The stock pickup was good, but sounded a bit hollow. Moving to a nordstrand (which are quite inexpensive), the bass has a lot of beef in the mids and a bit more aggressive upper mid character. My MIJ is super resonant and with that pickup and some flat wound strings it has just a massive sound with plenty of presence. I love it and have had it for a few years, but for what they are going for on the used market, if I were shopping sight-unseen, I'd probably go for a JMJ or American Performer.
To be honest, I like all of them, and they all have their place. Since you are coming from a p-bass, the simplicity of the JMJ might be just the thing, and that pickup and the broken in feel are awesome, but it doesn't sound like a pbass. For a more versatile, more refined take on the mustang, I'd go for the American Performer. For vintage correct, the MIJ or Vintera are cool, or if what you really want is an all-rounder/most p-bass like, the PJ is cool (and the most affordable) too. None of them are bad basses.
