I just tried a game as a proof-of-concept. Deity, islands, standard size/speed. Picked Rome so that I wouldn't be getting any unique bonuses.
First thing I did was delete my warrior for 1gpt. With no ruins/CSes and very late luxuries (had to wait for AIs to find me), I was still able to pump out 10 triremes and upgrade them all to caravels when astronomy finished around turn 100. Sent them all to my nearest neighbour with an embarked scout following.
There was no resistance. Cities and archers do 1 damage to caravels, trebuchets and triremes do 2-3. Caravels do 10 damage to a trireme, and 2-3 to a trebuchet or city. (Capitals are harder, but there's only one per enemy.) And with 7 speed (+1 from commerce), they never die, you just retreat back once it gets hurt. City falls to 1hp in 2-3 turns of bombardment, depending on how much coast is available to actually hit it, and I was mostly just waiting for my embarked scout to catch up. Once scout gets there and takes the city, injured caravels can now heal. A few cities later, navigation finishes, and they can upgrade to frigates. Game over.
This strategy is silly. The AI has absolutely no way to hold it off - and neither would a human player (unless he was doing the same strategy). And this was playing as Rome, with no bonuses whatsoever. Doing it with England would be ridiculous.
Considering how many cannon was on a typical frigate, why wouldn't' they dominate land units?
Because you can't actually shoot the land units very well. Perfectly flat shorelines are rare - usually there are sand dunes, trees, buildings, something in the way. It's pretty hard to actually aim at anything, especially considering that by definition, you are at sea level, so you are always shooting upwards. Land cannons, on the other hand, you can usually position on the edge of a hill - even a very small hill (so small it would be considered flat in Civ) presents a huge advantage. Also, waves tend to be larger closer to shore, compounding the aiming difficulty, and you risk running aground.
Edit: Sorry, I somehow managed to miss Thalassicus' reply...
Crossbows and Trebuchets are stronger than Caravels, and an earlier tech level:
I think you are underestimating the power of a caravel's speed. They have 7 moves with no terrain variations (you'd always take the +1 from commerce). In terms of which unit is stronger on offence, there's just no comparison - crossbows and trebuchets have 1-2 moves outside friendly territory, and trebuchets can't move and attack in the same turn. One on one, caravels and trebuchets seem about evenly matched. However, due to their 7 moves, it's very easy to get 5 caravels to instantly kill a trebuchet, and pretty much impossible to get more than 1 trebuchet to hit a caravel in the same turn (they need to set up, and caravels with +2 sight can see them coming). The lack of healing isn't a problem - just take the most exposed city first, and use that as your healing spot.
I also feel that despite being further down the tech tree than trebuchets, caravels are much easier to get. The techs along the way are much more useful in themselves (and they also include all the science techs, so you'll actually get there faster). Also, navigation is only one tech further, and caravels now upgrade into frigates. Finally, trebuchets cost 50% more hammers and require iron.
I don't have any comparison with crossbows, since I didn't encounter any in my game. Lots of trebuchets though, all of which were easily avoided and sniped. Sometimes they hit me, but never more than 1 shot in a turn. I feel crossbows would do slightly better, but not by that much. Longbowmen would probably do well - which makes picking England and ensuring no one else can have them even more powerful. CKN won't be better than regular crossbows since standing on the shoreline gets you sniped, while standing 1 tile back means you won't get that second shot. City+trireme+CKN can do a lot of damage, but by pulling damaged caravels back, you can still take it without losses - and even if you lose one, they're cheap to replace and reinforce quickly.
These units can defend against the 2 caravels I suggested earlier, but they can't defend against 10 caravels. At best you can pick off 1-2 for each city you lose, but you can't stop them taking all your cities, and they reinforce so fast that it doesn't really matter. You only have about 20 turns before they become frigates, making your life even harder. Eventually some will get logistics, and 7 moves + 2 shots + move-after-shoot makes them completely unkillable. They'll even take down artillery just fine (even in vanilla).
I'm going to play a full game as Elizabeth, and report back...