In which context is the word "libation" more often used?
I'd say the only use outside historical journals is what Fowler called 'Wardour Street English': self-conscious anachronism. So you might, meeting a friend, say "Care for a libation?", and if you receive an affirmative answer, go into a bar and say to the barman "Ho, landlord, two beakers of your finest ale!" Be warned, though, that a joke like this can permanently scar your vocabulary (mot to mention the danger of a faceful of beer).
In general libation and libations have been falling out of use:
http://ngrams.googlelabs.com/chart?content=libation%2Clibations&corpus=0&smoothing=3&year_start=1800&year_end=2000
However, both meanings refer to some liquid poured out to be drunk. The original meaning was:
The pouring out of wine or other liquid in honour of a god; concr. the liquid so poured out; a drink-offering.
But gradually this was broadened a bit to also mean:
transf. (somewhat jocular). Liquid poured out to be drunk; hence a potation.
The context will determine whether the drink is for the gods or not. However, both words seem archaic now. If you use either in conversation, people may think you are speaking in jest. That being said, unless you make it habit to discuss rituals about God, Jesus, or another deity, it is more likely that you would refer to libations as alcoholic drinks in general.
As @simchona noted, the word libation is not so used nowadays. Looking through the hits of the Corpus of Contemporary American English (restricting myself to news and magazines, because they tend to reflect contemporary use more than fiction), I find examples with either meaning:
Plan ahead. Visualize ordering that last send-off libation about an hour before closing time (and withstanding the arm twisting from your buddies when you demur on the next round). — Men’s Health
This idea alone attracts thousands to Cabbage Key in Florida each year. There's something about being able to pull right up to the dock and enjoy a nosh of comfort food - and possibly a libation - while taking in the waterfront scene. — Motor Boating
We have waged wars too often, preferring to fund them on borrowed money, and placing on most of us but a small burden-save for countless grieving families in this land who have poured out the lives and bleeding, maiming wounds of thousands of sons, daughters, husbands and wives-like a libation upon the altar of war. — America
"Before we begin," comes the West Indian accent of the dashiki-wearing bookseller, as he lifts a bowl of water, "let us pause to offer a libation to the ancestors. We'll have a moment of silence." — Denver Post
Overall, however, the meaning of “religious ritual” is mostly confined to academic-style writing about religions, rites and anthropology. It is also used in literary style, to create an emotional effect (see the America example). In everyday speech and writing, the meaning of “alcoholic beverage” is predominant.