Which has the advantage over the other? Is there any difference?

There are simple differences b/w them:
Threating Roar:
If you activated in response to an attack, that declared attack will still go trough, so you'd better use it before you opponents Battle Phase, nevertheless this gives the opportunity for your opponent to change his strategy.
Waboku:
Does not stop monsters like Mystic Swordman lvl2, nor it stops your face-down monsters from being forced flipped by an attack, altough its quite chainable.

Threatening Roar:

Waboku:

I say Waboku...

-Shane

Threatening Roar in my opinion, can protect you from much more. Whilst Waboku misses a few things, but covers that "first attack" that threating roar cant chain to, and stop.
Yay for big scary bear, which is another reason Threatening Roar is better. :)
Thank you,
Azurai Aeon

EDIT: IMO, I feel the text for Waboku could of been done better, its a little confusing, am I right?
In part in which, why I think Threatening Roar is better. Just have to do it in Main Phase 1 or before.

I personnaly have a greater preferance for waboku. That ability to chain mid-battle gives it the edge... So what if it can't stop Mystic Swordsman... Take the one loss and move on. Waboku lets you see exactly where your opponent is taking his attack before you launch a defense.

Waboku. Activate it on your turn and attack a monster with the same attack points as your own monster, and only the opponent's monster will be destroyed. Threatening Roar isn't a bad card though.

There have been posts on this debate already here.

But here's my updated take on it anyway.

Waboku:
Overall, better chainable card. Reduces Battle Damage to 0. Built-in Kishido Spirit/Kaiser Glider effect. Stall card. Effect Damage still applies. Monster effects involving battle still apply. Doesn't stop burn.

Threatening Roar:
Chainable. No attacking means no battle effects activate (DD Warrior Lady, Assailant become DD Nothing). Much more effective stall card. No Battle Damage (if timed properly), no Effect Damage. Doesn't stop burn.

One more card I think should be considered:

Hallowed Life Barrier:
Chainable. Waboku + Effect Damage coverage = 0 Damage...period! Discard can help, but mostly hurts, but also depends on the hand. Super Rare hurts your pulling chances.

I like Threatening Roar and I run it with Waboku, but the chainability factor carries a heavy weight. Waboku gets my vote.

Weeeell... Threating Roar May stop battle, but could also lose a chance to destroy a monster (Kyser glider like effect) But Waboku will be wiped by trap jammer (Curse you TJ, CURSE YOU I SAY!) it depends on your stradagy, i presonnally run Waboku over TR..

Threating Roar is better then wabaku because it stops all forms of attacks.

~ Davis

I like Threatening Roar. I mean, it saves your monsters from Mystical Swordsman and the like, which are seeing more play recently. Plus, it will keep your opponent from setting off your flip effects during your turn.

Threatening Roar is the better card here. You can activate it as your opponent enters his battle phase, to prevent all possible attacks. Don't forget, if your opponent doesn't declare going into the battle phase and just announces his/her attack, he/she rushed through steps so you can use the Replay rule and use Roar at the begginning of the battle phase, anyways.

Presonally I like Threatening Roar better. Are their arguments to be made for both cards? Sure. But at the end of the day, Threatening Roar fits my play style better.

I'd much rather be able to play Threatening Roar if I have a Magician of Faith face down on the field so I can keep the element of surprise until my turn. In Traditional Threatening Roar is even better since you can save Fiber Jar for your turn and potentially use it to gain a direct attack.