First I want to say I'm by no means an elite player. I've been playing Greece from day 1 and came back after a long break to test the new patch. I'm still able to beat Deity consistently using the same core strat I used before. I understand that the setting matters a lot, mostly I play conquest on crowded maps (large continents with 19 AI/28 CS), standard speed with default settings.
If there is one thing Greece can do better than any other civ is farm xp from CS (Mongols being the second best). By exploiting the UA, Greece can get elite units faster than anyone. My whole strat resolves around getting my units to level 5 as fast as possible. Without going into much details, basically, by exploting the Greece UA I usually have 2 swordsmen lvl 5 (march), 2 lvl 3 (medics) and 2 lvl 5 archers by turn 60 and 2 or 3 lvl 5 cats before turn 100. Ranged units with logistics/range and indirect fire, even archers, will give you complete control over the battlefield for a long time.
Maybe it's my playstyle, but as fas as conquest goes, I feel that a well balanced elite army beats mass-pretty much anything (specially fresh, not promoted units). While mass keshiks or whatever will give you a big advatage and allow you to go on a conquest spree, eventually unhappiness will become a issue and force your army to a halt. I would rather have an army composed of fully upgraded infantary/tanks/artillery when industrial age hits instead of a lot of fully upgraded tanks and a bunch of low level inf/art. When using other civs and focusing on science I'm able to get artillery faster than with Greece, but with Greece I'm able to get a fully promoted artillery (upgraded cannon) way faster.
I tried hardcore xp farming with other civs, and while it's quite doable, it just takes more effort/turns/units. No one can do it as fast and effectively as Greece.
Call me stupid but I don't understand how Greeces UA helps with xp farming. Could you elaborate a little?