No doubt - advantage for compiling the regular expressions only once. But I'd take it just a tiny bit further - instead of all the copying around of the line:

#list of regex-strings
my @regex =
(
    's/(a+)/\U$1/g',
    's/([bz]+)/XX/g',
);

#is now a list of subroutines
@regex = map { eval "sub { $_ }" } @regex;
[download]

Notes: got rid of the copying of the line in and out, we'll just work on the global $_; also got rid of the extraneous assignment to the global $sub variable. Now you use it like:

my @text = 
(
    "aaaabbzz",
    "bbbyyy",
);

for ( @text )
{
    print "org $_\n";
    for my $re ( @regex )
    {
        &$re();
        # or even just &$re
    }
    print "new  $_\n";
}
[download]

The advantage here is when you have many regex's (which the OP said they would) - less copying of data around. It's just a tiny bit more dangerous since so many functions modify $_, though.