So I'm hesitant really to answer this question, because I think there's a lot of issues with the way the problem at hand is conceived. I'm going to do so anyway, and I hope the issues will make themselves clear, but I should preface this whole comment by noting that strictly speaking the question is not really asking what it thinks it's asking.

Greek and Roman shipwrights in the Mediterranean from the end of the Archaic Period were able to build ships that, on paper, were every bit the equals of early modern ships of trade and exploration, and in very many cases vastly superior. Well over a thousand wrecks of ancient trade ships are known in the coastal regions (up to about 40m depth) of the Mediterranean alone, and many more are becoming known in deeper waters. The vast majority of these by far date from the third century BC to the third century AD, precisely the period of safest transit across the Mediterranean, made possible by Roman control of the sea lanes. We find most of the basic elements of ship construction for the next couple thousand years fairly early on. Mediterranean cargo ships were keeled, with ribs and crossbeams, and built typically using shell-first construction, with metal fastenings. Skeleton construction is increasingly attested in the Principate, and techniques such as interior keels, double planking (sometimes with different kinds of wood), and so forth were common in antiquity, as was the habit of metal sheeting of the hull (typically using lead). One ship, off the coast of southern France, shows remains of a sheet between double planks and an interior coating of protective paint, but no signs of exterior sheeting. Most ships, both warships and cargo ships, in the Mediterranean used steering oars, but the single rudder was known and is attested in river vessels. Multiple masts were known (two seems common by the Roman Period, though three masters are attested), as is fairly sophisticated rigging, and lateen sails, spritsails, topsails, and so forth are known alongside the more typical large, singular rectangular mainsail. Decking was sometimes continuous and sometimes partial. Multiple decks or banks were at least possible, as the existence of banked warships tells us, but I'm not actually sure how well attested multiple decking is among cargo ships.

These techniques of ship construction resulted in a fairly large variety of ships. The typical Mediterranean cargo ship was somewhere between 20-150t and of quite variable length and width. That's quite a wide range. For example, one Augustan period ship out of Minturnae carrying at least six individuals (Passengers? Crew?) that capsized south of France measured about 18m in length and came in at 45-50t. Another from about the same time in the northern Adriatic measured 21m length and 5.62m width, but came in at 130t. These measurements are comparable with early modern ships. A quick Google search suggests that Vasco de Gama's fleet consisted of ships with capacities between 50t burthen at the lowest estimate of the smallest ship (a caravel) to about 200t at the highest estimate of the largest ship. It looks like there's some disagreement there--I don't have the training to know the sources here--but the precise numbers don't matter all that much, that's fairly typical. Google gives the size of de Gama's flagship, the São Gabriel, as 25.7m length, 8.5m beam, and about 100t burthen. The precise accuracy of those measurements aside, this ship would have been a few meters longer and wider than the typical Mediterranean cargo ship, but on paper comparable. Compared to some ships of antiquity, it was at least theoretically tiny. Hellenistic kings and the occasional Roman emperor (Caligula) built enormously large ships, mostly to show off. Hieron's massive Syracosia, described by Athenaeus, was in excess of 100m length and was too large for any existing port but Alexandria to harbor it--as a result, Hieron gave it as a gift to Ptolemy. Ptolemy Philopator later built a forty, carrying some four hundred crew, four thousand rowers, and three thousand marines, which Plutarch says was so large that it could not really move. But one need not look so far, or even to Demetrius' fifteens and sixteens, to find enormously large vessels in the ancient Mediterranean. The largest of our shipwrecks yield ships in excess of 40m length and 450t. A first century BC monster off the Ligurian coast came in at 500-600t with a cargo of over 13,000 amphorae. A similar ship, off southern France, measures 40m length, 9m width, and has a capacity of around 400t--this ship was found with 6-7,000 amphorae in its hold. A late second century or early first century BC ship carrying 70 marble columns and assorted stone and bronze works of about 350t measured 40m length, 14m width, and 6.5m height. A wreck near Pisa, whose height we can also assess, measures about 14m length, 4m width, and 9m height--for some reason this ship was quite tall.

So these ships could come in quite large, with widely varying shapes, sizes, and layouts. The various technologies of European shipbuilding were at least theoretically known in antiquity. But the problem here is that all this on paper doesn't really mean very much. Roman shipwrights knew of decently sophisticated construction, rigging, and knew of such technologies as lateen sails and spritsails. But, for example, those two sail types were largely restricted to smaller vessels, even despite fairly sophisticated rigging on multi-masted vessels, the impressive rigging and sail arrangements of modern ships was almost completely unknown. Rarely would a mast handle more than two sails, and the typical arrangement of your usual two-masted Roman cargo ship consisted of a main mast with a mainsail (and sometimes a topsail) and a foremast with a small rectangular sail or a yardsail. Rudders were at least known by the later Principate, but typically not used. The largest ships were typically quite long, but very skinny, and lacked entirely the massive multi-decked castles of carracks, though some of the larger Hellenistic warships boasted actual war towers. By comparison carracks and other similar ships were often not especially large (though frequently much wider), but they had much more advanced systems of rigging featuring mixed sail types, single rudders, were much higher, were extremely stable and seaworthy, and were extremely maneuverable. Size isn't everything, and in fact early modern ships of exploration were not really terribly large at all: you'll find in any number of high school textbooks little diagrams that show the enormous size of Zheng He's treasure ships (many of which were smaller than Roman vessels) relative to Columbus' ships (which they dwarfed), but with no accompanying context.

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