I really enjoy Ethiopia in its current state because of the flexibility and early game bonuses. I absolutely hate picking a civ that has a UA/UB that requires something specific and then lacking that thing at the start of my game (ie, Iroquois without forest/jungle). And while there certainly are some uniques that scale better into the late game (Polands', for example), I find that snowballing out of the early-mid game does more for me than hitting a power spike in late from a middling position.
I do get that, in a sense, Ethiopia is very generic. There's no special pzazz or super unique flavor that you can't get from any other civ here. But I think that Ethiopia is unique in that you'll virtually always be able to come out of your early game with a strong position and fast religion, and quickly reach whatever tech you need to take advantage of your local resources/neighbors. And while it is brain-dead easy to benefit from the UB and fairly simple to use the UA, I feel that optimizing tech timings and choices in order to take advantage of the potential power spikes granted by the free techs does require a good deal of thought and planning. To be fair, if you just "do stuff" you'll probably get like 75%+ of the maximum benefit anyway- hence being a fantastic choice for newer players.
Personally, I love being able to go into a game not yet knowing how I will play it. On Emperor difficulty, progress, authority, and tradition have all worked for me, and I'll take any depending on my start. I can certainly be aggressive early (and often enjoy doing so), but unlike civs who gain access to their UU very early in the game, I don't feel cheated out of my special power spike if I feel that my start calls for passivity/peace until later on. Early expansion feels great (who wouldn't want to build as many Steles as fast as possible???), but consolidating and going a little bit taller/thicker can also work very well due to the ability to skip shrine and start producing other buildings or units more quickly. One of my favorite aspects of this is the ability to combine a tech rush with the fast pantheon; gaining access to quarries or plantations or fishing boats super early feels especially awesome when the associated pantheon comes with it.
Maybe the fun will wear off for me with more experience, but I dunno. I have had success with other civs, but I always consider old Haile for my next game whenever I finish a run.