I think I may have sussed my problem. Both times WC has stopped running, there have been dozens of references to a Teamviewer service trying to start. I deleted this application months ago, but there were still some stray com files in my library.
I have now deleted all these stray files, over 100 in total, and I'm keeping my fingers crossed that the problem is solved.
Apart from that, El Capitan seems ok to me, though I haven't noticed much difference. I've not needed to use any of the new features yet, but the new system font does seem much cleaner and crisp.