I started trying to think of situations where a person can have a wrist-worn PC but cannot have a handheld PC with them -- situations where people are constrained for some reason.
The obvious thing most people come up with, is where it's a natural or convenient constraint. You don't want to be holding something extra while you're swimming or swinging an axe or climbling a cliff. I think the related applications are already well-discussed.
What about when it's an artificial constraint? I initially drew a blank on how such a constraint would emerge, until I considered situations where the served parties by the two PCs are different, so that the handheld (if one is present) might serve the user (or manufacturer) but the wrist-worn serves someone else.
Once you start thinking of situations where the user is in an adversarial (or seemingly or potentially adversarial) relationship with the owner then it gets easier to see the applications.
Prisoners, parolees, etc. It's not so much that you let them wear the Pebble or iWatch, as you make them wear it. And your prisoner doesn't need to be surfing the web or otherwise doing things where the PC needs to communicate things to the user, so many of the disadvantages relative to handhelds, become totally irrelevant. The application, of course, is monitoring: being an open spy for the government.
Somewhat similarly: children. Mom wants to know where you are, but isn't really interested in giving you Yet Another porn terminal. Quit fapping and get back to your homework at the libra-- your friend's house?!? Get back to the library!
Marketing. Get 'em cheap enough, and these could replace your "frequent shopper" cards as your cookie. Wear our wrist PC as you walk around our store and check out, for a 2% discount. The application is spying, again. And I guess as long as it has a speaker, it can play location-triggered ads. "Whoa, you just walked right by our delicious canned spoo and instant flarn. Are you sure you don't want some?" The idea here is that you could perform the application with a handheld, but the existing handheld PC would be too pro-user so it might not really play the ads out loud and it might report false travel data. So you want the pro-store computer to be a physically different one. Then it becomes a wrist-worn simply because that's smaller and cheaper ($10 instead of $100).
Sweatshops. The Slurm factory employees are spending too much time on bathroom breaks, and texting their friends. Well, the employee wearable PC doesn't do texts, and it delivers a shock after 90 seconds in the bathroom. If a supervisor ever sees you without your wearable, you're fired.
Jealous spouses. Hubby's "Love Watch" chemical sensors are picking up interesting volatiles: perfume? My, he sure is breathing hard and the GPS has him in a residential neighborhood, not at the mid-town office. Oh, those are just fringe use cases: everyone knows the real purpose of the Love Watch is that it instantly relays every time you speak "I love you" into it. (OMG, that last part is so sickening that I bet a variant of this product already exists today.)
Think in terms of why you might want to "plant" (though not necessarily with subterfuge) your computer on someone else, to be your agent rather than the wearer's. Those may be the best applications for wrist-worn PCs.