Neck tension is something I have been aware of for some time and try to eliminate it. I don't think I tuck my chin when I breathe but I'll direct my attention to that possibility the next time I swim. Actually I often feel as though my right side breath is better than my left, but of course this could be my imagination. It definitely requires conscious thought, though, whereas the left breath just sort of happens. Sometimes I'm not sure whether I've just taken a breath or not.
It keeps me occupied for a half hour or so anyway.;-)