a) choose the most skillful person for the job, no matter how prickly or arrogant their personality
b) choose a lesser craftsperson in favor of having someone around that you can stand to be around
It's a tough call. I know a car repair shop owner who had to let a guy go once. The guy was an excellent mechanic, honest, skilled, good at dealing with customers, but he had the fatal habit of chasing women around the shop - in particular, the owner's wife's niece, who was working there. Bad move. He lost his job because he just couldn't stop reaching for the nookie jar.
We've all had people working on things for us who were abysmally dreadful to be around, and yet, when they (finally!) drove away, or you were rolled back to the recovery area, it felt good to have things fixed correctly.
And then there are times when you really enjoy being around the person, but they have not a clue about what they're doing. This is an absolutely true story: before fate led me to the wonderful Dr Neal Naff, King of All Neurosurgeons, the man who restored my back to its pre-injury glory, I spent some time with another surgeon, who earned points at least for honesty by saying, "I see what your problem is, but I have no idea how to fix it."
We don't hear that very often. And perhaps we should.
Take this simple test. If you want a critical surgery done, or your house rewired or a drain cleaned or your engine tuned up, you wouldn't call Regis Philbin, now would you? Sure, lots of fun, good to be around, wonderful chap. But not the man for the job.
And by the same token (we hear about this token all the time, but never get to see one) if you want someone shot in the face, call Dick Cheney! He's a proven professional in that field. You wouldn't want to be around him, you'd never think to call him to go to Red Robin and grab a burger, but he's got the skills you seek.