Enterprise wins. Its a capital ship the size of an aircraft carrier. Oh yeah...it has shuttles that can double as fighters. Type 12 phasers that are more destructive than any turbo laser and guided photon torpedoes...which the explosive component is ....ANTIMATTER!
The Enterprise has more firepower and the Millennium Falcon has a hard time with TIE fighter and Han and Chewie always try to avoid Star Destroyers, which in terms of size is more comparable to the Enterprise
yet they get heavily damaged by one lame damn hit every time in every series rendition of the ship. for a so called advanced ship they are weak as frick. the falcon is to for what it is but at least its got mobility than a giant pizza cutter with neons.
the reason is cause 1. the falcon is meant to be a smuggling ship than a fighting ship but 2. the enterprize is a research ship more than a combat ship. sure its heavilly armed but its more made for comfort than fighting
not sure if I am remembering wrong, but I think that their teleporter things cant go through shields and since star wars shields tend to actually work compared to star treks lame ass useless shields......you get the picture. I love star trek as well as star wars but the whole shields to maximum, get hit ONCE and suffer major damage every time is just lame.