Star Wars is more political, the Prequels alone are proof of that.
I disagree. The prequels more so but this comment was made in rearguards to the originals.
Star Wars does deal with a political struggle (the rise and fall of fascism/empire), but in very broad terms. Star Trek on the other hand continually explores deeply political issues. Political concepts are debated and poured over. Examples that spring to mind are:
Journey to Babel - delegates from different societies with different types of relationships
Let That be your Last Battlefield - racism
Justice - how much respect should the laws and beliefs of other cultures be given?
Symbiosis - where to start! Ethics everywhere. The nature of the drug supply problem, plus how much should we (Starfleet) get involved
Measure of a Man - human/android rights. It's basically Amistad in space.
Suddenly Human - the rights of a child to determine their destiny vs. that of their biological family
The Drumhead - MacArthy style witch hunts based on one's backgroud
The Defector - clue is in the name
Unification - an ambassador working to bring together two peoples who were once one.
The list goes on and that's before you get to Deep Space Nine, where it might be easier to list the episodes that were not political in nature.