I will be judging this round based on the criteria of: rants.
It really comes down to Tyler's lye burning scene and Vizzini's battle of the wits for me.
Communication of Character
Tyler communicates a great deal of his worldview in his rant - and crafts a compelling picture of a fucked up dude by way of his rationalizations to boot - whereas Vizzini's rant largely communicates that Vizzini fancies himself a clever man, skeptical and well-read. I have to give this one to Tyler - when it comes to letting the character tell the audience about himself, you walk away knowing a lot more about Tyler Durden. With Vizzini, you pretty much just learn that he's Sicilian. And kind of racist.
Tyler 1
Vizzini 0
Quality of Rant
Vizzini's rant is a dazzling display of deductive reasoning, from which the entertainment is found in following along with Vizzini's logic. It is very entertaining indeed, up there with some of the funner passages to be found in the canon of Sherlock Holmes. Tyler's rant is a different kind of spectacle - he doesn't so much earn your attention as torture it out of you, but once he has you there, he uses it to great effect. Vizzini is entertaining, Tyler is enlightening. I'm going to give it to Vizzini, simply because he can toy with his mark for longer at a stretch.
Tyler 1
Vizzini 1
Strength of Argument
Unfortunately for Tyler, I don't believe his "connect the dots" argument-building would hold up very well without such a captive audience. "Our fathers were our models for God - if our fathers bailed on us, what does that tell you about God?" This sort of tactic would fall apart quickly in any proper debate, and with good reason. Meanwhile, Vizzini crafts and incredibly compelling argument for his ultimate decision in the game of wits... but you can't really get around the fact that he was, ultimately, wrong. Sorry boys, no points.
Style
It was over before it started. Sorry, Vizzini.
Tyler 2
Vizzini 1
Quotability
I can't speak for anyone but myself, but while I can more-or-less remember the high points of Tyler's rant, it's the narrator's contributions that I remember more. ("I try not to think of the words searing flesh.") On the other hand, "never get involved in a land war in Asia" is timeless. Point Vizzini.
Tyler 2
Vizzini 2
X Factor
As far as rants go, I'm ultimately more compelled by Tyler's than by Vizzini's, but with the caveat that it's largely dumb and bumper-sticker-y. Platitudes, rehashings, etc.. Vizzini's rant is entirely spur of the moment and synthesized from Vizzini's current experience, which is impressive in its own right. So then. I'll call the X Factor in this round "if not for an external reason to be there, who would I listen to for longer?"
Tyler 2
Vizzini 3
The game goes to Vizzini, and The Princess Bride.
The Matrix vs. The Princess Bride
Teague Chrystie
I have a tendency to fix your typos.