It usually comes down to building a catapult vs building another composite bowman (unless you have some OP UU). Cata's are great with an early "army" of 2-3 CB/chariots, 2 melee or mounted, and their effectiveness scales exponentially the more of them you can move in on a given turn. They give you two things: earlier city capture (good for the surprise), and fewer units lost. A couple of cats can give you a two-turn capture instead of a 5-turn archer volley.
On Emp-Deity, you won't expect to bring catapults against anything less than composite(s) and 30+ str cities. It's rough. But, as suggested there are a few effective strategies.
If you can get pikemen, they are the best damage soakers at that stage, with no real counter... they come late though in early war. Cover is an awesome promotion, as is defensive terrain. If you can move and attack the city on that turn (or likely another unit nearby), they will take just enough damage and survive long enough to soak two turns worth of city bombardment.
Horseman can be great at this also, because they truly wear a "kick me" sign on their back, and they can pillage twice per turn (barring ZOC and terrain) to heal up far more than the pikeman, and you can withdraw them easily.
By the way, if you build a catapult, you should never lose it. Ideally, put a barracks behind it because as soon as you get the second promo, volley increases its city damage by 50%! It's not easy to get these units xp in the early game. If I can "powerlevel" them off barbs en route to war (usually for the first cat as the second one is building), I will always try to pick up volley. In any case, don't let cities kill your catapults. Back them off if they are at risk, and park them on a mined hill so they can pillage heal+bombard in the event they are targeted.