Rangers or Elves? I think the "Elves" category is a bit too large. There's all sorts of Elves. Just being an Elf didn't make one a great tracker because different Elves excelled at different things. I think it's likely that some Elves were good trackers and other Elves were not.
As far as individual trackers go Beleg seems to be comfortably in first place with this quote-
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for the skill of Beleg was greater than any that have been in Middle-earth
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And I also believe that Aragorn should be quite high up on the list considering-
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And my search would have been in vain, but for the help that I had from a friend: Aragorn, the greatest traveller and huntsman of this age of the world.
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Though the word "tracker" was not used, the context of this quote specifically involves the tracking of Gollum. After all it calls it a "search" which would certainly imply tracking. Not to mention that "huntsman" would overlap much with tracking. In fact, when Aragorn, Legolas, and Gimli are tracking the orcs from Rauros they are referred to at least once as "hunters".
I think that Aragorn possibly is the greatest tracker living in Middle Earth during the War of the Ring (and I also think that Tolkien might've intended that quote to mean that he was). Elves having sharper senses doesn't automatically make them superior trackers.
For example, Turin obviously showed that men were capable of evening up the playing field with Elves. Even with a big mob of men following him around who were less in skill than he was, he still managed to elude the greatest tracker in history (Beleg) for quite some time.
Rangers vs Elves? Rangers, I imagine. After all, tracking was their life, where as many Elves probably never had to track.
Rangers vs Elvish trackers? Tough one. I believe the origin of the Elf would have to be taken into consideration. Rivendell likely had trackers to rival the Rangers (I'm fairly confident that the sons of Elrond could), Lorien might have as well, and who knows about the Mirkwood Elves. But certainly there would be individual differences.
And when it comes to individual Rangers versus individual Elves (during the time that the Rangers existed) I'd have to go with Aragorn unless someone can persuade me otherwise.
(when considering all the ages of Middle Earth however I'd definitely pick Beleg)
<font size=1 color=339966>[ 3:28 PM February 03, 2004: Message edited by: the phantom ]