The goal of the Libertarians isn't to "beat" the leftists...
...or at least, not in the sense of eliminating their candidates from the political process. If it were, then I could agree that Libertarians should bury their differences with Republicans to elect as many non-Democrats as possible.
But the goal is not to do that, but rather to restrict government and enhance liberty (social and economic) to make a free society. Republicans and Democrats occasionally do right on one of the two aspects of liberty (social or economic) but rarely (if ever) do good on both, and often do bad on both.
Hence if you actually want to change the system, or at least change the meta-context in which the system makes decisions and decides what is important and what is taboo, then you need to vote your conscience and not "strategically". The two major parties have made their life's work manipulating folk into voting against the other side, hoping that there are just enough strategic voters out there to manipulate with scare tactics and promises of Nirvana if only their side could win it all and banish the "wrong-thinkers" from the political arena.
If the Republican Party had actually carried through on the Contract w/ America and cut back on government, I might have been voting for them these past years. They betrayed me and anyone else who loves liberty almost as soon as they got in power. I will not vote for a party that cannot live up to its promises (smaller government, etc). The Republicans haven't cut a dang thing from the government, and ironically non-defense discretionary spending has gone through the roof with the arrival of a Republican president.
Not much of a difference, aside from national security (which Democrats, at least since JFK, don't have a clue about).