Uhh, I dunno where you get your Information Vis, But I have Justice and Joyeuse on PLD and i have Swung 4 Times (2 with Each weapon) More times than i can count.
Maybe your unlucky, or not paying attention, But they both can definitly proc on the same atack round.
You can triple attack with this, Double attack proc + the weapon's extra hit, which makes it better than Joyeuse. The str+7 is just a bonus.
Edit:
According to Wiki this is 10% more likely to proc its double attack than Joyeuse
@Aluus
I don't know where you get your info from but you ~CANNOT!~ double attack or triple attack with Joyeuse if Joyeuse's initial effect kicks in. You are prob seeing 2 different attack rounds close together that it looks like one but infact is 2. That happens very often due to low delay of Joytoy+Haste+Haste equip.
You need Virtue Stones to activate the latent effects on this weapon and all other weapons dropped from the jailers in Sea. Uses up one stone each time it proc's.
@Itachi
Dunno where you get your info but that works with Joyeuse too. Ask any RDM who's ever sported Joyeuse with a brutal earring in campaign. Need proof? have em use a tier 2 enspell. it only procs on the first hit. occasionally you will see 3 hits, the second 2 without enspell dmg