Both the high and the low precedence logical operators have their own pitfalls, so you have to be careful anyway.
Having said that, I find that the low precedence logical operators express much more often what I want, probably in more than 90% of the cases, so that's what I am using most of the time. Also, since they are so low in the operator precedence list, I most of the time don't need to look up the documentation to find out if I am right.
So, even though I tended to use the high-precedence operators when I picked up Perl, because of my background with C and C-derived languages, I quickly moved to and, or and not.