re: Star Wars vs. Star Trek in a battle for all the marbles...who wins?

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The Federation isn't nearly that big. It's merely 8,000 light years in diameter. 

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Not only that, but Starfleet itself is small. In Kirk's era, he said there were only 12 "starships" - ships like the Enterprise - and they are widely scattered. In Star Trek The Motion Picture and The Final Frontier, the Enterprise was the only earth ship that could be spared for the mission. In the Search For Spock, the Excelsior was the only earth ship the Enterprise had to worry about escaping.

Even in the TNG era, it was rare to see ships as advanced as the Galaxy class Enterprise. Most were movie era ships, which would have been close to a century old.

In First Contact, the Federation musters a fleet of a dozen or so ships against the invading Borg. I just don't think the Federation has what it takes with withstand an Imperial fleet.