As regards the original question, fleets do vary widely in size. A typical fleet from the War of the Vespers in the Mediterranean, one of the most important predominantly naval conflicts, might have been a couple of dozen galleys with 200 men each. Each fleet at the Battle of Sluys, part of the Hundred Years' War, probably consisted of 200-300 sailing ships (in this case, mostly cogs) with an average of several dozen men each.
It's actually more to do with sailing conditions in the Mediterranean as opposed to say the North Sea. Enclosed seas such as the Med, Baltic and Black tend to be much calmer with far more predictable tides and winds than vast open seas such as the North or Atlantic. Try taking a galley into an open sea and it'll be sunk in the first squall.
Not entirely true. England built galleys in the 13th and 14th century. France deployed galleys in Boulogne in 1339 and had Genoese galleys at Brest in 1342. Also, Viking longships are very similar to Mediterranean galleys, and have very low freeboard, yet they managed to ply the northern seas very regularly.
My impression is that any power in either the Atlantic or the Mediterranean which was serious about seapower
and could afford to do so built galleys, up until the late 14th/early 15th century. Oared ships are much more maneuverable, and they usually carried significantly more men.
Also, a galley fleet can beach. This means that it can act in coordination with a besieging army to cut off a city from the sea.
Finally, although a galley has to worry about low freeboard, it does have one advantage if bad weather is brewing -- it can seek shelter much more easily, both because it can beach itself and because it can row against the wind.
However, oared ships are expensive, because you need rowers. They have smaller cargo capacity, because they need to be low to the water to be rowed efficiently. They have a more restricted cruising range, because they need to put into shore for water every couple of days, or even more frequently if the rowers are exerting themselves.
Wooden ships rot, so if they're not paying for themselves by running cargo, the cost of maintaining a fleet can really add up. Even though England built galleys, I'm not sure if they were ever used in battle -- probably they rotted before they were useful, or the trained rowers needed to man them wandered off because their pay was in arrears, or because of some other typical medieval snafu.
Things seem to change a bit in the 15th century as medieval shipwrights started to be able to build some really vast watercraft, like Henry V's Grace Dieu, that would have been very difficult to attack with a low-lying galley. However, these warships would also have a hard time attacking a galley, because it could just maneuver out of range. Cannon do not seem to have factored into ship design until fairly late, although no doubt they were mounted.
Galleys seem to die out in the Atlantic after 1400, although they persist in the Med as the premiere warship until the early 17th century. You also find them in the Baltic and even in the Great Lakes until the 19th century. So clearly rough seas are a factor, but not the only factor, in determining whether or not a given navy opts for galleys versus sailing ships. Technology and the economy also make a difference.
If you're interested in design, a typical Mediterranean warship would probably be classed as a bireme by the ancients. It is very low to the water (half a meter at midships, plus a railing) which makes it much more efficient than most ancient ships. So, a medieval galley can carry 200 men of whom 100 are rowers, and because they're all one one deck they can double as marines. A Greek trireme has 170 rowers and only 30 marines, and the rowers are below deck.
Medieval hulls were more flexible than ancient hulls and thus probably impervious to ramming, so instead ships mount a "spur" (like a ram above the waterline) that can be used to crush the oars and possibly the railing to make for easier boarding. Although they are very low to the water amidships, they can probably mount a small "castle" at the prow and stern to make up for the height disadvantage. Your standard galley would probably have two main lateen (triangular) sails, which I think would be taken down and stowed for battle.
This is a good reconstruction of a dromon from around the 9th century, taken from John Pryor's Age of the Dromon via Wiki. Unlike a medieval galley it has one bank of oars below decks, which would make it a bit slower albeit somewhat higher out of the water.
This reconstruction has a Greek fire siphon mounted at the prow. Greek fire was a scary weapon but it's actual performance in historical sea battles was pretty hit-and-miss. Maybe wind conditions had to be just right before it was used. Consequently, other nations might have opted to skip the incendiaries and mount towers on the prow instead.
People still dropped all kinds of things on each other's decks, including slippy stuff used to make the enemy lose their footing. Uneven footing makes a big difference in naval battles, and probably gives the advantage to somewhat more lightly armored troops. Missile fire seems also to have been as or more effective as a melee advantage, with Catalan crossbowmen and English archers both seeming to be particularly valuable at sea.
Difference is, they didn't have an organised navy.
That is the key difference between northern and Mediterranean naval warfare. England and France did have organized galley fleets, but they were very small, and seem not to have been available when they were needed.
A galley fleet is expensive to maintain. It can only pay for itself in time of peace if the values of cargos was very high, and the risk also very high.
The average profit from a northern voyage transporting beer, grain, or some similar commodity was 25 percent. The average profit from a Mediterranean voyage carrying spice from Alexandria could be as high as 100 to 150 percent. Thus, it made sense to take the latter in a swift galley or convoy of galleys -- and it made sense for another power to try to intercept that spice convoy.
In other words, richer seas sustain more expensive fleets.
The same phenomenon helps explain why Baltic cities formed a league (the Hansa) while Mediterranean cities competed so vigorously against each other.
(Source, Hendrik Spruyt, The Sovereign State and its Competitors)
I've been reading a lot about naval warfare recently, and I'll try to post a summary of my observations at some point.
In the meantime, if anyone wants to read about galley warfare in a M&B-like time period, I highly recommend wiking/googling Roger of Lauria, one of the medieval world's most celebrated admirals.
I'd also expect most galleys would want to be beached, or at least anchored in a sheltered harbour overnight; I doubt they'd have enough crew to keep the ship manned on a 24 hour basis, and leaving the ship in open water while the crew was sleeping would be incredibly dangerous. Thanks to the requirements and space of sailing a cog carrying 'extra' crew for another one or two watches wasn't a problem, though their more robust construction would make sailing overnight generally safer, particularly out to sea (one of the main problem with galleys is they tend to stick close to the coast, where submerged rocks and sandbanks are a danger, both of which are hard to spot in the dark).
