Depends on what you want to do. Aura of Rightful Authority is straight-up mind control, and once it wears off, the target is going to be cheesed at you. However, for the duration, you can pretty much ask the target to do anything reasonable short of murder (or even that, depending on what the target's profession is), and they'll do it. Also - it's single-target, meaning that using it out in the open is going to get you noticed.
In contrast, Aura of Enobled Presence is passive, doesn't require that you cast it on anyone but yourself (and thus can be prepared beforehand), and just makes you look better - to the point where while the effects of the Gift are still in play, people will react more positively to you.
So - Ennobled Presence: better for long term interactions with people (ie, recurring NPC's in your saga), while Rightful Authority is best for adventuring and putting the mind-whammy on solitary guards and whatnot.
In terms of overcoming the effects of the Gift: neither of them do - the only thing that does that is Gentle Gifted. With Rightful authority, they treat you like a boss - one they hate, but feel obliged to follow. With Ennobled Presence, they consider you a smarmy used car salesman or politician - they find you annoying and manipulative, but they'll put up with you anyway. (EDIT - as opposed to suspecting that you're a serial killer sizing up their liver to go along with some fava beans and a nice chianti.)
EDIT - also, it depends on your playstyle. I've found that most players/GM's tend to downplay the effects of the Gift, as most NPCs they interact with (ie, grogs) are used to it. Yeah, they're SUPPOSED to still take the -3, but I've found that most groups tend to ignore that detail. As such, if you're using Aura of Ennobled Presence, you'll have to remind people that it's up, and that people should be reacting to you differently than the other PC's - which is kinda annoying. However, if you have some long-term game mechanics (such as the Covenent rules on grog satisfaction), you can use Aura of Ennobled Presence to justify a +3 reputation with your servants....assuming you always have it on whenever you speak with them. (Not actually all that hard, as that is probably just for 8 hours a day or so, which won't get you long-term warp.)
In contrast, Aura of Rightful Authority is an active ability to use - so you'll use it less, but it will be more useful to have when you need it.
Personally? I'd take Ennobled Presence, as I'm honestly not a big fan of mind control: I treat is essentially as equivalent to attacking someone with a deadly weapon, and use it with that kind of restraint with most of the characters I play.