A couple of people in the past have said that they didn't notice that you could combine units together (place L1 on L1 to get L2, or L1 on L2 to get L3 - must be the same type of unit)
It's about the only thing i can think of to explain why the AI would have them any faster.
Generally speaking, L2 units are going to be the "backbone" of your army, required to attack enemy towns, and good for defending important points, L3 are (usually) only useful to break enemy lines if they have a lot of castles, or to protect a critical spot.
L1 mainly get used as a cheap way to capture undefended tiles.
In any case, if that's not the reason, i would look at differences in play style between yourself and the AI - it may be getting the L3 units faster, but does it sacrifice having the numerical advantage to get it? (in which case the answer is simply to try to surround and cut it off).