This looks like production code, so I'll assume you want not golfed code, but better abstraction. And it is sort of expensive, so you might want to use a Schwartzian Transform.

sub by_priority {
    my @prio = (-1 => $a, 1 => $b);
    my @prfx = map { (qr/^$_/)x2 } qw(Organization Service FAQ);

    for(@prfx) {
        return $prio[0] if $prio[1] =~ /$_/;
        push @prio, splice @prio, 0, 2; # swap (-1 => $a) and (1 => $b
+)
    }

    return 0;
}
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Capture regularities in code, irregularities in data.

Update: oops, thanks BrowserUk. I had used @match rather than @prio at first and forgot to update all locations. Hope it's clear now.

Makeshifts last the longest.