The Usenet Oracle has pondered your question deeply.
Your question was:

> Oh mighty oracle, who CAN eat just one potato chip, please tell me
> this:
> 
> We've got a betting pool going on with regards to famous matchups in
> history.  Who would have won these?
> 
> Bach vs. Beethoven
> Rembrandt vs. Van Gogh
> Aristotle vs. Kant
> Da Vinci vs. Kepler
> 
> (just so you know, my money's on Bach.)

And in response, thus spake the Usenet Oracle:

}  The Oracle resurrects Aristotle and Kant, and places a open bag of
}        Ruffles before each.
}  
}  Orrie:  "Now, who can eat just one?"
}  Aristotle:  "Why would anyone not want to eat just one?  One is the
}        measure of all things, from which all else is built.  One is
}        unity, and symbolizes purity.  Therefore clearly I could eat
}        just one."
}  Orrie:  "Yes, well you still haven't tried them."
}  Aristotle eats a chip, and another, and another.  "Mmmm.  Very good."
}  Orrie:  "Hah!  So you can't eat just one."
}  Aristotle points to the bag of chips.  "This?  This doesn't matter.
}        What matters is thought, and a have logically shown that I can
}        eat just one."  [munch]
}  Orrie:  [turns to Kant]  "How about you?"
}  Kant:  "Clearly we can't discover anything by just thinking about it.
}        We must perform an empirical experiment."  [Eats a chip.]
}        "Yes, I this is evidence that I can eat just one.  However a
}        single experiment conveys little information.  We must verify the
}        results." [Eats another chip.]  "Yes, this corroborates the first
}        experiment. Still, more evidence would be helpful."  [Eats more
}        chips.]
}  Orrie:  "It appears neither of you can eat just one."
}  Aristotle:  "What!  I have logically proven that I can eat only one."
}  [munch] Kant:  "And I have-"  [munch]  "-performed many experiments
}        showing that I can eat just one."
}  Orrie:  "Thank you gentlemen."  *POOF*
}  
}  Oracle writes down on clipboard "Aristotle v. Kant --- both lose."
}  
}  Orrie:  "Hmmm.  They ate all my Ruffles.  Now I'll have to perform
}        some different tests."
}  An art dealer suddenly appears.  "Zat am I doink here?  And zo are you?"
}  Orrie:  "I need you to appraise these."
}  Dealer:  "Zwa?  Es dis an original Rembrant?  And dis a Van Gogh?  Vere
}        did you get dese?!"
}  Orrie:  "The curator of the Hermitage had a question... But that's
}        another story.  Which is worth more?"
}  Dealer:  "Dese are both priceless!  Rembrant and Van Gogh zere both
}        brillant painters!"
}  Orrie:  "Yes, but who's the _winner_?"
}  Dealer:  "Vell, de Van Gogh ist probably vurth more, because Van Gogh
}        painted less.  Ee ad a miserable life, you know."
}  Orrie:  "And Rembrant didn't?"
}  Dealer:  "Yes, dat's right."
}  Orrie:  "So Rembrant was the winner, but if you want to be a winner
}        you'll own the Van Gogh rather than the Rembrant?"
}  Dealer:  "I suppose...."
}  Orrie:  "Thank you."  *POOF*
}  
}  Oracle writes down on clipboard "Rembrant v. Van Gogh --- Van Gogh died
}        penniless and insane.  Rembrant wins."
}  
}  A musician suddenly appears.  "Hey!"
}  Orrie:  "You're a classical musician, aren't you?"
}  Musician:  "Yeah.  Who are you?"
}  Orrie:  "I'm the Usenet Oracle.  You owe the Oracle a autographed
}        original of one of Mozart's compositions.  And try to grovel when
}        you ask a question."
}  Musician:  "What's going on here?!"
}  Orrie:  *Zot*  "Remember what I said about grovelling?"
}  Musician:  "OWWWW!  Ouch, oww."
}  Orrie:  "Who's more popular, Beethoven or Bach?"
}  Musician:  "Geee, I don't know."
}  Orrie:  "Who's more widely known then?"
}  Musician:  "More widely known?  What do you mean?"
}  Orrie:  "Who's work reaches the farthest?"
}  Musician:  "Well, Beethoven's Fifth Symphony is on those records that
}        NASA puts on those space probes."
}  Orrie:  "And Bach's work is not?"
}  Musician:  "Not that I know of.  But they also have 'Johnny B. Goode'."
}  Orrie:  "Thank you."  *POOF*
}  
}  Oracle write down on clipboard "Bach v. Beethoven --- Bach loses to
}        Johnny B. Goode.  Beethoven wins."
}  
}  Orrie:  "This is too much work."
}  Oracle writes down on clipboard "Da Vinci v. Kepler --- Da Vinci is two
}        words and seven letters.  Kepler is only one word and six
}        letters. Da Vinci wins."
}  
}    Supplicant, here are the results you wished for:
}        Bach vs. Beethoven:  Beethoven wins
}        Rembrandt vs. Van Gogh:  Rembrandt wins
}        Da Vinci vs. Kepler:  Da Vinci wins
}        And in philosophy no one wins.  Remeber that philosophy majors
}                when you get out into the real world.
}  
}  You owe the Oracle some bags of Ruffles potato chips to replace those
}  eaten by Kant and Aristotle.