1- ottomans
a- UB, hamam is great. +2 happiness and +2 health just enables you pop-up your cities population higher early in the game, and if you combine it with monarchy/representation, you get quickly growth-cities which is cool
b- UU, janissarry is cool also. they come with gunpowder (without any resource need) and has +%25 against all other units except siege ones. with proper promotions they hunt every unit without any problem.
Drawbacks: you should get UU as quick as possible to use it efficiently. although they can easily dominate the era they are in. UB, is (kinda) not efficient in late game. after a time, you should be able to handle happiness through resources, trade or luxuries slider after all.
2- Byzantium:
a-their UU is great IF you have iron&horse. once you get them, your enemies will become like bugs to you. in early-mid era you just go hunting (different version of Prateorions

)
b- UB is also good. it alone gives you 2 happiness with only one slider movement.
Drawbacks: if you dont have iron or horse forget about UU. if you have enough resources for happiness or get them through trade or monarchy etc. UB doesnt have significant effect on any time
i just mentioned about civs though. in the end leader is more important than civ, who decides your game-playing style