In one case you stringified it. In the other you are taking it in scalar context and Perl magic is not doing what you expect.

use strict; use warnings; use 5.010;

my @array = qw (there is some data here);
is_empty (\@array);

# look out for edge cases
@array = qw(one);
is_empty(\@array); 

#empty it
@array = ();
is_empty (\@array);

sub is_empty {
    my $array_ref = shift; 
    say "\nGot: ". join ", ", @{$array_ref};
    say "Empty" unless scalar @{$array_ref};
    say "Caution"           if $#{$array_ref}     ==  0;
    say "Empty"             if $#{$array_ref}     ==  -1;
    say "Maths == String?"  if @{$array_ref}      ==  "";
    say "Empty as String?"  if @{$array_ref}      eq  "";
}
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Cheers,
R.