Best Star Trek film of all is the second one "
Star Trek II : The Wrath of Kahn" (at least until I see the new one in early May.) Next in line would be "First Contact" with the Borg - an absolute riot.
I would follow this by "
Star Trek VI : the Undiscovered Country". (the favourite line of mine in this movie; Favourite line is by Chang quoting "
Shakespeare is good in English, but you need to read him in the original Klingon ...", and saying "
taH pagh taHbe' " ("
To Be, or Not To Be") - Klingons loving Shakespeare because "
everyone dies"! Classic.

(I.e. Hamlet is Klingonese is at;
http://www.khemorex-klinzhai.de/e/Hol/kli/hamlet )
Best Star Trek episode of all is "
In the Pale Moonlight" in Deep Space Nine (Series 6) and is some of the most intelligent sci-fi I've seen on TV. The story goes along the lines of tricking some others to rally towards someone cause, and in turn throw away your morals and values to achieve it. I can still vividly remember the great quote by Capt. Cisco ;
"My father used to say that the road to hell is paved with good intentions. I laid the first stone right there. I'd committed myself. I'd pay any price, go to any lengths, because my cause was righteous. My... intentions were good. In the beginning, that seemed like enough."
If I were to second guess, it would be "
City on the Edge of Forever" in the original series (Series One), followed 3rd by the quite pleasant
Star Trek: Enterprise "
Carbon Creek" (Series 2).
The best Star Wars one is the first Episode "
Star Wars : Episode IV A New Hope." It is fun, it pure escapism, and when I first saw it at the cinema as a teenager took my breath away.
As for the best between "
Star Trek" and "
Star Wars", well there is no answer, because each must be taken on their own merits. They have there good points and bad, but if you let yourself go into the imaginative world, then as long as they entertain, they are all mostly very good indeed.
DRAW, methinks!
Note: However, if I had to defend myself in a fight, give me the Star Wars lightsaber any day over Trek's Klingon bat'leths (sword of honour) and phasers. 