Hidden combat penalty on deity vs cities?

My city has ~40 combat strength and a crossbow. Napoleon attacks it with a few musketeers and crossbows and some chariots. He easily takes it unless I defend it with my army.

Egypt has a 37 combat strength city with a chariot archer in it and he already lost his entire army. I have 2 trebuchets, 6 knights, 4 crossbows, 2 pikes and a general. After his city kills my trebuchets (he targets them first unless I have wounded units ) I simply don't do enough damage on the city anymore... Melee-ing it is not an option because it does like 0 damage and it hurts my units too much.

Huh? Did I miss something? When my knight attacks his city my knight loses like 80% hp. When Napoleon melee's my city he loses like 20-30% hp? Not to mention his damage against my city... is like 3x more. Or does egypt perhaps have a lot of +hp buildings in the city that I have not?
No I do not attack over a river or anything.

Am I totally wrong here and missing something or is there some hidden combat modifier?
I also noticed that Napoleon always avoids my army. When I move my army to city A he moves away to city B and when I move or chase him he just goes to another city even though he has no visibility on my army. Could be pure luck though.

There are a bunch of combat modifiers, but none is hidden.

Your knight has -33% against cities and the game tells you so.
Naps troops might have had +50% vs cities due to promotions (unlikely). More likely: Your city was weaker and his troops stronger (more cs, no cavalry penalty) than what you compared it to in your attack.

There also the Oligarchy policy from Tradition which makes garrisoned AI cities very hard to capture without losses.

PS: You probably should just "suicide" your knights I with that I mean let them attack once. Then the AI will kill 2 of them in the first round. When it's your turn again pillage tiles to heal them a bit (they'll still be the targets next round). This makes you easily get 3-4 rounds of shots with your trebuchets and crossbows. Next time: Don't build more than 1-2 melee units (they're only needed to actually take 0 hp cities).

Thanks, that explains a lot. Can't believe I missed the -33% cavalry penalty.