Ancient beer had no hops, which was invented in by medieval European brewers. In English, the word ale was used for beers without hops. Nowadays, ale refers to top-fermented beers. African folk beers or Finnish folk beers, like Sahti, are probably the closest you'll get to ancient beer. Because of the lack of hops or other flavorings, the beer is supposed to taste grainier and kind of like liquid bread.

Modern wine is actually pretty close to Greco-Roman wine in terms of the process used to make it, although there is one major difference: the Greeks and Romans always used to dilute their wine with water, so that they could drink more while still maintaining a civilized atmosphere. You can find Greco-Roman style wines all around the Mediterranean. One common one is mulsum, which contains honey and herbs as flavorings.

Source: A History of the World in 6 Glasses by Tom Standage

I can tell you with almost cerainty that ancient beer and wine would have all been sour and murky/Unfiltered. Without modern sanitation, wild yeast and bacteria will ferment wort (unfermented Barley tea) or must (unfermented grape juice). These usually are a blend of brettanomyces, lactobacillus, and pediococcus; and unfortunately acetobacter. Brettanomyces creates Phenolic or yeasty funk like wet hay and molding grapefruit. Lactobacillus and pediococcus create lactic acid during fermentation which is what makes a sour dairy character. Acetobacter creates acetic acid which is precisely the same as vinegar. So your drink would be Unfiltered and murky and would be certainly funky and sour.

Edit: I should elaborate that the yeast and bacteria above is native to the skins of fruit and vegetables and will simply start fermenting once in a medium of starch and water that is room temperature.

Edit 2: If you look hard, many craft breweries today make sour ales with precisely these fermenting methods. For wine, any of these "infections" are considered faults so will be hard to find. But if you try home brewing your own beer or wine, undoubtedly you will have batches that turn out funky and sour.

Source: I'm a home brewer, not a historian.