or does the use base take care of this?

base does not prevent you from overriding the parent's constructor. Nor does it prevent you from doing something silly like blessing the object twice. Fix:

package Child;
...
sub new {
    my ($class, $arg1, $arg2, $arg3) = @_; 
    my $self = $class->SUPER::new($arg1, $arg2);
    $self->{arg3} => $arg3;
    return $self;
}
...
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Also - is there a difference between

Yes:

• base doesn't load Exporter.
• base will load Parent if it's not loaded (or silently fail).
• base sets @ISA at compile.
• base doesn't disable strictures for @ISA.