Beer built the pyramids. That is how the workers were paid, they weren’t slaves, just workers and farmers,on the off season.
Not much of one, however. Not a single “revenuer” died, but 3 or 4 tax protestors went to 'the bad place"… 
It should be noted that distilling wasn’t invented until some time in the Middle Ages, so it wasn’t an option for ancient civilizations.
Wine was one of the major reasons international commerce developed, though.
I guess this is the right moment for all of us to raise a glass or two to the memory of Abu Musa Jabir ibn Hayyan, Maria the Jewess, and Aeneas Coffey.
And I also vote for beer. As Benjamin Franklin is supposed to have said: proof that god loves us and want us to be happy.
No argument, but read the OP. Civilization was the keyword I believe.
Beer the cause and cure of most of man’s problems.
Homer Simpson
For grape-based wine: Vinegar and verjus, beeswing(cream of tartar), and if you don’t pick grapes in time, raisins.
Beer built the pyramids. But wine lubricated the symposia, and the Roman Empire (And the Greeks and Persia).
Vines needs more management and care than grain does, and I’d argue that’s a benefit, not a negative, socially.
Even with refrigeration, not all that long.
I keep popcorn and rice and barley in my pantry. They all keep for a year or more with no refrigeration. Granted, i keep them in sealed containers, but… You can’t keep beer in a burlap sack, either. And even in my fridge, beer goes bad. Waaaaay faster than grains spoil.
The value of beer is that it makes barley and wheat palatable, not that it makes them easier to store or protects them from pests. The value of beer and wine is partly accessible calories, but mostly that people like to consume alcohol.
And as for the economics of which is better, that varies a lot with the weather and some with the soil.
There’s some important qualifiers there. The burlap sack doesn’t keep out moisture, bugs, or mice nearly as well as a plastic bag. Also, modern grains go through industrial drying and in some cases milling processes, which were not as effective or available in the past, to remove spoilable elements like husks and bran. They might also be specific cultivars with exceptional storage longevity that didn’t exist until the modern age. Those grains all take up a lot of space on the scale of a farm, if not a pantry, and it’s much harder to keep pests and spoilage at bay in quantities that can’t be visually inspected without literally digging through large piles of the stuff.
My rice and barley have been milled. But i suspect that’s a fairly old technology. My popcorn hasn’t, which is why i brought it up. Popcorn can’t be super dry, either, because it’s the water in the grain that makes it pop. When it gets to old and finishes drying, it doesn’t pop properly.
I’m certain that pottery vessels can be fashioned that exclude mice. They are probably less challenging to make than ones that contain beer. Insects and rancidity are more challenging issues. Of course, you can still eat grain that has some insect damage. And i wonder if roasting grains in a pot could kill insect eggs …
But have you ever tried storing beer? It really doesn’t keep well. I’m not much of a beer drinker, but sometimes people bring it to parties. Leftover beer goes bad. And not in a useful, vinegary way. I find it really implausible that beer was ever an economically viable way of extending the storage life of grain. I suspect people made beer year round from stored grain because they liked beer. Just as they made bread year round from stored grain.
Maybe it’s just modern beer that goes bad?
Please see this post:
But not long term storage.
Keep in mind some of the ancient beer also had a lot more solids in them, making the beer truly breakfast in a mug.
Why It's Actually Important To Check Beer Expiration Dates.
This says 6-9 months if stored air-tight. Heated grains will store longer than that air-tight.
One of the virtues of grain in early agriculture is that they store really well. Also pulses.
I’ve read that in some societies, beer provided a really large fraction of all the calories and many other nutrients consumed by most of the population.
That’s a feature, not a bug. 
Insect contamination of grains was a source of B vitamins and why modern grain products need to have vitamin supplements added.
Also called legumes. (In my dialect, a pulse is what the nurse measures. Not something you eat.)
As I pointed out in post #8
Barley grows nearly everywhere. It was a very early crop and has spread almost everywhere people have. Grape vines can’t and haven’t.
For northern regions wine was an expensive import.
One of the problems with talking about beer is that its got a history that’s thousands of years old scattered across multiple cultures. Just here in the United States, beer drinking today isn’t the same as it was in 1830. But essentially I think you’re correct. There was some non-local trading of ale in the medieval period, but I think most beer produced was consumed locally and not too long after the brewing was complete.
Which brings us right back to wine being of additional value in the promotion of trade.
Seeing the ingenuity of humanity when it comes to finding ways to have fun and/or alter our state of consciousness, I fully believe that all the considerations of social betterment are a beneficial side effect of our more self-indulgent desires.
Which is fine, I mean, how much of our current tech is based on someone growing up watching Star Trek and the like and dreaming of one day having the same gadgets?
I only bring this up because we could do the exact same discussion of the merits of nearly any issue/development from pre-history to the modern era and try to track down sources and do a cost/benefit analysis.
After all, this topic leans towards GD as much as FQ, in that the comparative benefits are contextual and at this remove in history, subject to a great deal of speculation and emerging/changing evidence.
And we’ve not touched on alternate fermented but not distilled beverages, since the OP only specified the two.