Long term: Will probably not make things worse for very long, so in the long-term it's better than full-bore rage but not as good as walking away.
Side: If your child is doing the yelling and screaming, then your refusal to react at the same angry uncontrolled level provides a useful model and will actually help to develop calmer behavior on the child's part in the long run, but the harsh expression will still be inflammatory.
The Rational Saint: Exhibiting inhuman restraint, go to the child and in a gentle voice explain why what she is doing is not the appropriate way to treat her parents and/or ask her to explain why she's misbehaving so terribly. Like Shock and Awe, a common but largely ineffective response, and when serene self-control evaporates in the heat of battle, the Rational Saint often gives way to Shock and Awe.
Immediate: Your explaining will not make the crisis worse and will help to end it more quickly by not being provocative, which is better than a rage reaction but not likely to change the behavior. If you invite your child to explain, you will probably prolong the crisis, as she will take the opportunity to further elaborate her point: "Because you're a jerk! Didn't you hear me?"
Long term: Your modeling of calm in response to rage will have a positive influence over time, but the effect would be slow to occur, and few humans could keep it up for long.
Side: Your refusal to react may be calming, but that alone will not teach the child the proper behavior. Also, by moving in close to explain, you leave yourself open to being hit or pushed, and few parents can take that without reacting. Still, if you can restrain yourself, you will feel that you are wonderfully controlled and empathetic—and you are.
The Ringmaster: Divert your child's interest to something else to get him out of crisis mode. Hand him a toy or, if he's older, attempt to engage him in discussing whether anyone shreds more rulingly than the guys in DragonForce.
Immediate: Not likely to work at all, but if you present some wildly novel gimmick it could reduce the duration of the misbehavior. Of course, next time you have to come up with a fresh gimmick. No human can keep this up for long.
Long term: No effect. Distraction does not change the likelihood of future occurrences.
Side: Avoids the task of teaching other ways to handle stress, but you do show restraint by not fanning the flames of rage.
The Void: Ignore the provocation and walk away.
Immediate: Withholding all attention de-escalates the child's behavior and so is likely to end the child's comments sooner than would be the case if you responded in a heated fashion.
Long term: Ignoring—known technically as "extinction"—could slightly decrease the likelihood of disrespect over the long-term, but its effect is still weak. The best benefit of this option is your modeling of a nonimpulsive reaction.
Side: You're modeling poise under fire, but you are likely to view it instead as a weak response that passively accepts abuse, so you'll be unhappy with it.