Here's what my research has come up with....so far.
There are a couple things we must keep in mind. Keeping fruit juice more than a couple days in the climate around the middle east without refrigeration would be a futile attempt at best as it would spoil rapidly. Fermenting it into an alcoholic drink was a means to preserve the beverage for longer periods.
To make wine in its plain form one would ferment the grapes allowing the yeast to consume the natural fruit sugars and produce alcohol. Depending on the variety of grapes used, where they are grown, and how ripe they are when harvested, the resulting wine will typically have an alcohol content somewhere between 10% and 17% naturally (i.e., without adding any additional sugars).
It should also be noted that it was only recently (last century or so) that yeasts have been been developed that can survive in alcohol above 13% so prior to that development, 10% - 13% was typical. Today's wines, however, can be stronger with alcohol content ranging up to 20% by volume.
Picking grapes earlier when less mature will usually result in a lower alcohol content simply because the fruit has not produced the sugars needed to feed the yeast. In some cases the resulting wine can be as low as about 5.5% alcohol by volume. About the only way to get lower alcohol content and still call it a wine is to somehow remove the alcohol that it contains or dilute the beverage with water but then you also lose the preservative quality and the drink will spoil more rapidly.
So, even if we go with the idea that alcohol in Biblical times was at 5.5% by volume it would still be stronger than an average American beer. For example, here is the ABV rates of some of our more popular beers. Trust me, one can get drunk quite rapidly on any of these. I remember a time when I drank 3.2% (3-2 beer) and getting drunk was not difficult even at that low alcohol volume.
Miller Light - 4.2%
Miller High Life - 4.6%
Bud Light - 4.2%
Budweiser Select - 4.2%
Busch - 4.3%
Busch Light - 4.1%
Michelob Ultra - 4.0%
Michelob Light - 4.1%
Micholob - 4.8%
Milwaukee's Best - 4.1%
Old Milwaukee - 4.5%
Coors Light - 4.2%
Hamms - 4.7%
Strohs - 4.5%
Corona Extra - 4.6%