Best - Ethiopia. I don't get why people think they're weak. Neftenyas shred all other infantry units once they get the dumdum bullets card (including skirmishers and redcoats!) and even before that they're stronger than redcoats in small numbers despite only costing 20 coin. They do have problems countering artillery, as rotary cannons have short range and they don't have any really strong cavalry, but they're otherwise very strong.
Worst - Of the ones I've played, Serbia. No eco bonuses, setting fire to buildings is very rarely useful, no particularly strong units, and it's difficult to micromanage the economy.
I agree with the Ehtopians. They are my favorite. You mentioned the cav, that they are not really strong. But in my opinon the Oroman horseman are doing a very good job, but also the Escorts are strong with that range attack and bonus againts artillery. You get them to 47 dmg with 14 range and 2 times dmg againts artillery( and 3 times against handcav). This is strong.
A weakness from the ethopians ist the long building time for the units. You have to build a lot of building to get enough units in the fight. The eco is so strong (micro skills needes unfortunately) so that you are definetly fine with 70 settlers. So it is hard to react and to manage what unit you should build and mix. All in all I love this nation
With the serbians I also had problems, because I needed to much space with the fields, cause the need to grow when they were build. Also a little bit complex that you can't see your upgrade posibilites, so you have to know all and decide what you gonna use and what building you have to have.