There is some debate on whether the larger maps are more difficult than the smaller maps. It kind of depends on your playing stlye, difficulty level, and what type of map (land mass/water %), your playing.
I play pangea maps, Regent-Monarch level so here's my perspective:
On huge maps, when you have 16 civs, science does seem to go faster. They have adjusted the tech rate for map size, but it may not be adjusted correctly. With 16 civs, you have all the expansionsit civs in the game. One expansionist civ gets a tech from a goody hut and then trades it to everyone else, the next expansionist civ gets another tech from a good hut and trades it around. It doesn't take long at all before your in the middle ages. Plus with 16 civs, you have more of a possiblity of civs, going off and researching different techs, which will be traded and speeding up research more.
With corruption, getting more cities doesn't really make you all that much more powerful. It does to an extent, but after so many cities, and so far from the capital, those cities will be nothing but a 1 shield/1 gold land waste.
One thing about huge maps is that you usually have more time to prepare defensively for war, especially early in the game. Ancient era wars are a little harder, since it takes so long to reach your enemy. But with 16 civs it can be almost, or just as crowded as playing on a standard map with fewer civs.
Although, on the huge maps, if you have fewer civs (like 8), the AI spends so much time still in their initial expansion phase (building settlers) because of all that open land. You could seize this opportunity to attack them.