Imperial Hippodrome makes a lot of sense, especially against the Ottomans, because you are going to be dealing with Sipahi. With Triumph, your Horsemen do 13 damage compared to the Sipahi's 12, making them slightly better.

Longbowmen make a ton of sense against Janissaries because the additional range means you'll have excellent tools to deal with them.

Having Longbowmen means you don't have to worry as much about Janissaries, so you can actually go for Cataphracts and invest into cavalry instead of being forced into infantry only.

The Mehter's +2 melee armor aura makes Sapahi take significantly less damage from horsemen.

Byzantine Longbows can snipe Ottoman Janissaries. Against Ottoman cavalry raids, getting the Painted Shields upgrade on Limitanei gives them 1.44 tiles per second movement speed, making it much easier to react to raids.