There's far, far more drinking in Star Trek than Star Wars.
Yes, one of the most famous scenes from the original Star Wars Trilogy is in a cantina (though maybe Luke's getting the equivalent of an O'Douls), and clearly the fantastic character Han Solo appreciates a good drink -- even Obi-Wan does, as seen in the prequels. If I can cite the Expanded Universe, Timothy Zahn's Star Wars novels establish that they have whiskey. There are sports bars, at least for the people of the lower levels of Coruscant.
But so many characters and drinks simply don't seem to go together. I can't see Grand Moff Tarkin unwinding with a glass of pinot noir. Emperor Palpatine doesn't seem to me to be the imbibing type; he's just drunk on power. There is actually an online description (of course there is) of how Darth Vader got nourishment, and combining alcohol with that would be dangerous and pointless; he certainly wouldn't have enjoyed it. I can't picture off-duty stormtroopers doing shots (their aim would be bad, anyway). The Empire's ships and buildings are clearly drunk-unfriendly, with all those miles-deep drops and so few railings. Though admittedly this could be a galaxy without drunk driving/flying, so maybe this is all worth it for that.
It's not just Imperials. Can you picture Yoda having a beer? Even if his species' metabolism worked really fast? (Drunk Yoda is just too depressing an idea to contemplate.) At Hoth, drinks were almost certainly not considered essential supplies, so the selection at best sucked and likely didn't exist. Maybe that's why Rieekan had so much trouble smiling. Droids are likely incapable of imbibing, and considering they're (in some way) alive, they probably have a sense of what they're missing. Maybe that's why C-3PO's so uptight. But even the non-uptight in Star Wars rarely drink. IS ANYBODY IN JABBA'S PALACE ACTUALLY DRINKING? It's only implied (except in the sailing barge). Those sleeping palace denizens could just be really tired.
But in Star Trek, people of all species drink, and it's -- usually -- a good, accepted thing. The 24th century's Starfleet flagship has a bar. It serves everything, even prune juice. (I love that Worf loves prune juice. He called it "A warrior's drink.") And by the 24th century there's synthehol, which lets you feel drunk until you have to feel not-drunk, and you just shake off the effects. Klingons have blood wine; Romulans have that ale that Federation types even break the law to have (and that ale probably makes up for the general blandness of Romulan food); THE CAPTAIN OF TWO ENTERPRISES IS FROM A FAMILY OF WINEMAKERS. Two of Trek's most extreme cases of drunk behavior had nothing to do with alcohol but with a contagion aboard ships, in the original series' "The Naked Time" and Next Generation's "The Naked Now." Can't blame evil liquor for that! (We have to find other reasons why "The Naked Now" is awful, but that's a rant for another time.)
Maybe I can be annoyed that there's a stereotype where of course the Scottish crewmember is a hard drinker, but at least there's far more to Scotty than his drinking. (Riley, on the other hand...) And I suppose it could've been worse and shown Sulu drinking sake. So not all of the Star Trek drinking is entirely positive. And I'm undoubtedly forgetting many things in the giant Star Trek universe. And maybe I just could use a drink.*
Is it just that Star Trek's had more chances for drinking to come up? Canonically, I mean? Trek's had all these TV seasons -- 30, if you count the Filmation cartoon -- and 12 movies so far, while what's considered the "official" Star Wars story is in six films, the computer-animated and kid-friendly TV series (The Clone Wars and the upcoming Star Wars Rebels), and Brian Daley's radio adaptations of the original three films. The Expanded Universe (yes I know I cited it earlier) doesn't officially "count" -- the upcoming new Star Wars films Disney is preparing won't follow those works. The EU books could show that there's a version of Beer Pong played by Dia Nogas but no future Star Wars film or TV show would be locked into saying that that's a "thing."
This is, ultimately, one of many signs that Star Trek has always skewed generally older in its audience than the kid-friendly Star Wars (the original film of which almost got a G rating). There's more sex in Star Trek, too, and more positive forms of it than the relationship between Anakin Skywalker and Padme Amidala that in part leads to the collapse of the Galactic Republic around them. Of course, their kids will grow up to rebuild that republic (and kiss each other, but don't hold that against them), but that's a hell of a lot of collateral damage from getting it on. Compared to that, at least drinking in Star Wars isn't so daunting.
* By the way, yes, I'm posting this in the morning, but I wrote this Sunday in the p.m.