War has a much different 'feel' in this game than in the previous civs. Those pesky military nations can still be effective even if you have a tech advantage and you can conscript people into units early under dictatorship. Bowmen just don't mow down warriors, let alone spearmen, and defending a city seems easier that it has in the past. Knights and 'elephant' type units don't show up until the Middle Ages, and by then, most civilizations are well entrenched on their lands. Chariots are only 1/1/2! No stomping all around the world with them anymore, and barbarian goodie huts seem to only give out 2 hit point warriors (which are only good for scouting really). All of a sudden the Jaguar warrior doesn't look half bad, since you start with it it has ZOC and can manuever all over the map...chariots cannot pass through forests or mountains so can be very hindered.
All this means that the Ancient Times wars are going to be slow affairs, where your veteran swordsman slug it out with veteran spearmen defending cities...if you are trying to fight anyone in AT then you almost need Iron Working...swordsmen are the only real offensive unit, and even then only if you have a barracks to train them up. Fights can go either way regardless of the units involved as well, stack the odds in your favor repeatedly...no more stomping an entire civ into the ground with 2 chariots and a legion.
On the plus side, all of this applies to you as well...it seems to me that even the more warlike civs don't take to war early...I had the Aztecs right next to me and Jaguar warriors all over my map but they never harrassed my workers or settlers and didn't take over any undefended cities. Also ANY city is good for making units, you no longer have to worry about that city with 2 shields making a unit that would take one of those away...this is really nice, you should pretty much always be able to have a viable standing army to defend your cities.
Not to say that war cannot be fought early on, I did manage to wipe the Germans from the earth as the French (gotta love industrious/commercial) by getting Iron working and cutting off their supply of iron, but it was a long and painful process where I ended up with several German citizens that hated my iron fisted rule. Then I find out that while I was merrily fighting the English had sent out ships, contacted a bunch of civilizations, traded tech to Monarchy and started into the Middle Ages, while I was turns behind because I had many less-productive cities, not only that, but I had nothing to offer them but cold hard steel...while they were getting close to gunpowder! YIKES!