actually in that scene they were drinking Ale made in Rohan. Rohan is, per Tolkiens notes, inspired by the Anglo-Saxons. in Anglo-saxon culture, beer and Ale were fairly common drinks (mead and wine were the more high class beverages), and of the two both were relatively low in alcohol content, with Ale being the weakest of the two (beer was brewed with fresh mash, Ale was made from mash that had already been used to brew beer). given the common methods of brewing available to that tech level, the alcohol content would likely have been only a few percent perhaps 2-3% at most.. enough to ensure the beverage stored well (”old ale” was frequently mentioned in written documents, apparently the flavor improved some as it aged.) but not enough to really get people drunk unless they really worked at it. beer was not much stronger in general, perhaps twice as alcoholic as Ale.
The elves of mirkwood in The Hobbit were drinking Wine from Dorwinion, said to be a “heady wine” (a term referring to particularly strong alcoholic beverages.) and meant for small bowls. regular wine can get up to 15% alcohol, which would make it about three times as strong as beer, or about six times as strong as the ale the rohhirim were drinking. further, the description of the beverage in the hobbit actually sounds like distilled wine, known historically as “heart of wine” but better known today as Brandy. which can get up to 60% alcohol, and is usually thus served in very small amounts.
the Jailer and the Quartermaster were drinking Dorwinion wine in big flagons, and from the description in the scene, were drinking for several hours before nodding off. whether wine or brandy, that is a lot of alcohol.
which suggests that Elves are not easily effected by alcohol, and if legolas was faking anything, it was that the ale was having any effect on him at all.