Constants have the advantage of getting optimized away, when used as booleans in conditionals. Like this:

use constant DEBUG => 0;
if(DEBUG) {
    print "This will be gone.\n";
} else {
    print "Hello, world!\n";
}
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Using perl -w -MO=Deparse test.pl, the outcome is:

BEGIN { $^W = 1; }
use constant ('DEBUG', 0);
do {
    print "Hello, world!\n"
};
test.pl syntax OK
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with the equivalent code using Readonly,

use Readonly;
Readonly $DEBUG => 0;
if($DEBUG) {
    print "This will be gone.\n";
} else {
    print "Hello, world!\n";
}
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I get this instead:

BEGIN { $^W = 1; }
use Readonly;
Readonly $DEBUG, 0;
if ($DEBUG) {
    print "This will be gone.\n";
}
else {
    print "Hello, world!\n";
}
test.pl syntax OK
[download]