Uh, just analyze it Combat...
Even Shang HHA (no ballistics, no alchemy) will EASILY defeat Assy's HAs. They have 43 more hps and and extra attack point...most civs will have +43 hps AND +2 attack which is HUGE because all HAs get +2 shielding. In Hittite's case it's even worse: their HAs have +3 attack, +43 hps over Assy's. Not that I'd ever upgrade to HHAs anyway; waste of gold that is better used on Assy-killing 27s training time, 240 hp legions that take 40 shots before going down and cost nearly 1/3 as much, Cats that kill them in one shot or phants with 600 hps.
Assy is the slowest builder along with Phoe without architecture. That means it gets units out slowest. This more than negates its faster firing HAs. Not only that, elephants, towers, legions, catapults, and heles, all of which are popular DM units, will all murder Assy HA (which get killed by one cat shot, btw: no nobility also no alchemy and no chain mail for the heavy HA upgrade, so they're a bad choice even in archery). That combined with the fact that Assy is the slowest builder means they are one of the WORST dm civs. Sure they're versatile, but I'll take Bab's versatility, or Hit/Cho's power any day over the incomplete and slow versatility of Assy.
BTW Assy HA don't stand a chance vs. a Choson legion flood. Cho towers absolutely rock HA, and their legions train in half the time (the barracks builds 50% faster, and the legions train 13 seconds faster too)...so you're dead against a good Choson. Choson will very easily hit 200 pop limit before Assy gets to 100 units...lets see who wins now...besides how the hell will I have 10 villagers painting the map, I will have over 50 if I start the same way you do, but i get them out faster because my TCs have ARCHITECTURE. Oh wait my legions build twice as fast, so you will have 0 HAs pretty damn soon (especially if I'm smart enough to build towers to cover my foundations, which any good DM player will do...towers stop any HA rush COLD).
A good Hittite will have more archery ranges than you pumping HAs that have ALL the upgrades plus the bonus and can just overwhelm you with that and the supercats...not to mention an elephant rush. Same with summie, you give up 1 range no your archers but your army is nearly as powerful.
And then Bab, their archers are better than Assy's too (nobility means they can take an extra 2 hits and an extra cat rock + alchemy for flaming arrows that do +1 attack + they have architecture + their towers are annoying as hell to Assy). Their HCats can devastate the entire Assy army, and the legions/HA clean up anything in their way.
Rome too would devastate Assy w/ the awesome legions and great siege but since this is AoE we're talking about..
Greek/Mino just build up ur siege workshops and (very important) towers too to protect ur builders from HAs pinging ur building frames...after the first couple minutes its all smooth sailing as Assy's un-engineered siege can't touch Greek's.
Let's see Phoe Assy can probly handle...priests priests priests...both dont have architecture with really sucks...altho Phoe can take waterways with those juggs, there is nothign Assy can do against Phoe juggs..
Phant civs give Assy all sorts of trouble...they simply walk over all of your elephant counter units. Actually a phant trains nearly as quick as an HA and the architectured stable is built faster than the Assy ranges, so...I will have more phants than you have HA...and no matter what you do an equal # of phants ruins and equal # of HA. Also I just run the phants rite up to ur archery ranges, and anything that pops out is instantly killed by splash damage...then some phants wreck 20 houses and then you're kinda dead...
Yam/Shang are the worst in AoE but even they can give Assy a fight with architecture...pump out phracts and HHAs as fast as possible...they are better than Assy's units in the first few minutes.
There's a reason why AoE DM is only Hittite and Choson. It's because these two civs are clearly the most dominating civs in DM...