When you attack, you must not forget the Aid_system, where different type of troops supports other types in battle.Do I just need more units? (I have roughly 10 city attack units to their 5 longbowmen, but again, I don't seem to deal any significant damage regardless.)
Or do I need higher tech to break through?
If you can, try to make attacks with smaller stacks of say 3-4 different troops - fx 1 or 2 unit(s) with City_assult promotion, 1 or 2 unit(s) with a "+xx% vs archers" and 1 or 2 mounted unit(s) able to make some "Collateral Damage" - then make your attack. If you loose, replace the lost unit and attack again. If you win, replace the wounded unit with a fresh. Never attack with single units only, seldom (but not never) attack with a stack of same type of units. Never include units with no City_Attack support in the attack. *)
You will proberly need much more troops to do above.....
It's dang hard to take cities, that are defended with (any kind) of archers until you get access to the bombard. Specially if some of the defending archers has the City_defense, Drill or Hill promotions (last only if the city are placed on a hilltop of course).
*) Edit: That is - if you after your "normal" attacks have your enemy down on the knees - then it might be a good decision to give it a try anyway...........