"Balanced Resources"? I don't recall seeing that option anywhere on the startup menu.
So far I have played 14 games at Noble level. I won one (on points and on the second try), but lost the rest, placing well down in the pack. In all but one game there was no Bronze anywhere near my Capital, so I had to get to Iron Working before I could produce any worthwhile troops. In about 4 of those games, no Horses were nearby either. My strategy is now to go for the Oracle so that I can select Iron Working as my free Advance. Otherwise it just takes too long to get there, and I have to sacrifice most of the other early advances to acquire it. It's a . .. .. .. .. . when you have a Worker sitting doing nothing around because the tech isn't there for them to work on any tiles.
Correct me if I am wrong, but it appears that the AI's receive a bonus Warrior at the start, to guard their capital while their "normal" Scout/Warrior goes searching for Goodie Huts and resources. It also seems that they receive a bonus Archer when they build a city. I cannot believe that they can have 2 or 3 per each while I am desperately trying to balance building, research and recruitment. I am doing well to manage one Warrior/City in the early game!
Another thing that happens frequently to me is that the AI's start to really take off in the latter 500 years of the game. I usually manage to stay with them until around 1500 AD, then suddenly they are picking up Advances at twice the rate I can manage, no matter how much I micro-manage my cities and play with the sliders.