Ahhhh you just hit the Regent hump!
Seems to be a big jump in difficutly when you go to Regent. Can't ignore defences, build EVERYTHING in every city and take on the world with a handfull of units anymore, sorry.
There will actually be another such hump when you move on to Emperor.
On the lowest levels you and the AI are roughly at the same build speed. On higher levels however AI cheats and builds things alot faster than you.
Which is why you always seem to be outnumbered and every damned city you try and take has WAY too many units in it.
One good example of a game I had once, I was trying to go for a conquest victory so I was at war continuously. Towards the end, I had to go to war with basicaly the biggest superpower because they had nearly all the territory left which I needed to win. Towards the end of that war, it (carthaginians) had roughly 10 cities left, but at the beginning of each turn I would see about 15 modern armour come out to attack. They wouldn't do much because I litteraly had mech inf armies garrisoned in each town they could attack, all died on each attack. But each new turn of theirs there were another 15 or so modern armour built.
Now do the math, 10 cities 15 armour??? Something not right, how could they build more units per turn than they had cities. And in addition, how in gods name could any city build a modern armour in just 1 turn?! Especially since this was towards the end of the war, and most of the cities left were not quite the largest and most productive.
So yeah, like everyone mentioned make sure you have enough money to keep a large army, put a roads on everything, build only buildings you need. Build evenly too, make sure you don't build say a library in each city, build libraries in some, and markets in other simultaneously. Dedicate certain cities to ONLY build units, and don't build too many defensive units to put in all cities. 1 or 2 are good for the core ones as millitary police, and say 4+ or so for the border towns both as defence and as garrisons to move forward with an attack.
As what you do with captured cities, well I suggest you keep them them. They add to your income and everything.
Which means when you plan your attack, plan in such a way that you have pleanty of defensive units that can move up just behind your main attack. Some people don't belive in this and would actually just garrison with attacking units, but I don't. See the thread on border defence for example.