I normally don't like going through tunnels, even though I am not claustrophobic. I just don't care for the experience. However, I'd probably do the Chunnel, simply for the convenience, and to get to London or Paris that much quicker. I could deal with 20 minutes in a tunnel. I don't know that I could do much more than that, but 20 minutes would be all right. It would be preferable to a stormy Channel crossing!
I haven't heard about any incidents in the Chunnel in a long time, so I'm assuming they've worked the kinks out, as far as safety and construction go. I prefer to allow someone else to do the driving in any kind of tunnel, so that works for me.