stat has slightly less overhead, but File::stat is slightly more readable. File::stat is part of the Perl core since 5.004 (released 1997-05-15), so it's quite safe to assume that File::stat is available even on older Perl installations.
File::stat has some minor problems, mainly with the implicit $_ and the special handle _, see "Bugs" in File::stat. Also, the filetest operators -t, -T, and -B are not implemented in File::stat. This is documented in "Errors".
Today I will gladly share my knowledge and experience, for there are no sweeter words than "I told you so". ;-)