Ok... so, let's begin !
The original idea comes from a simple concept : the current UA bonus of Byzantium just goes so well with Arabia's imperial history, as did the Arabian current UA for Byzantium. As a consequence, I wanted to try to do something about this situation (which I did in my tweaks). Afterwards, ideas and reactions from other people gathered around this idea, and it also evolved in my head. The result is here for you to read.
Now, let's go piece by piece :
- Arabian UA : now previous Byzantium UA, without any change needed. It is powerful, flexible, and it shows well the impact Muhammad had on Arabian history (in so many ways).
- Byzantium UA : it has been nerfed on its most balance nightmare part (the GP part is just so snowbally it is difficult to conceive things around, so better axe it) and boosted in specific ways to allow for different strategies (the free Historic Event from Barbarian Encampment is not only thematic, it also allows Authority Byzantium to be a thing).
- Arabia UU1 (Guzat) : We have no early skirmisher unit in the early game, and having it at around the same time the Arabian religion should come online is thematic and it gives the civ a real springbox feeling. This, plus the lack of Horse requirement and the reduced cost, means that the unit shouldn't have much more combat power compared to the Heavy Skirmisher, or it would be oppressive. The Withdraw Before Melee part allows the unit to be survivable (and so gain more experience its in lifetime) and entrap enemy units which try to catch it without pushing the enveloppe too far.
- Arabia UB1 (Suq) : With the departure of the current UA from the Arabian kit, the Bazaar has to change. The idea there was to make the building a toolbox for the civ, with several bonuses that can be powerful when used correctly, but don't help the civ that much at first. The bonus Gold / Faith from followers of rival Religions not only punishes those who push the religious game too early against Arabia (for it will give the civ the Faith it lacks to gain its Prophet early), but also symbolizes pre-Islamic religious history in the region, and later the dhimmi presence within the Empire, with the advantages and challenges it represents historically and in term of gameplay (especially in case of conquests).
- Arabia UU2 (Baghlah) : Although I like the Hashemite Raider, I do think it comes too late to truly affect the game state. Arabian naval history, which had important effects on world history, was also underepresented, hence my choice for the Baghlah. In term of gameplay, it is a versatile (as is meant to be the rest of the Arabian kit) unit with lower economic burden (since it was used mostly as a commerce and pirate ship) and a wolfpack playstyle.
- Arabia UB2 (Dar al-Shifa) : Once againt meant to be versatile, this early version of the Hospital also comes with big advantages for those who balanced their economy well by offering potentially major Science and defensive bonuses. It is not flashy, but quite potent and rewarding.
- Byzantium UU1 (Cataphract) : Although powerful and interesting, I've always found the current version of the Cataphract a bit clunky : its minor bonus against Cities (-25% CS instead of -33% CS) takes design space for no interesting or impactful reason, and its bonus in flat terrain is so massive it creates a weird power spike for a unit that wants to be slow but reliable. I decided to go fully into the direction of a defensive knight (the kit is already geared towards playing tall and defensive) with the added bonus of providing surrounding units (especially ranged units) support to end the job (which allows the Byzantine front to be more stable) and some offensive power in flat terrain to still have our armored charge dream.
- Byzantium UI (Aplekton) : A mix of an original idea of mine and pineappledan's input, this improvement is meant to provide a direct counter to one of the most unfair ways an enemy can break the Byzantine turtle strategy while also giving some bonus yields (quite useful for new secondary cities), defense and good vision. With good technologies and policies, it can also become truly important in generating an important amount of science.
- Byzantium UU2 (Dromon) : I do find that, even in 4UC, the Dromon is a bit clunky. Its plague promotion, although interesting, is quite niche, and its one splash damage promotion alone isn't enough to make the difference I feel. This is why I decided to make the unit a true 1 range aoe terror with double the splash damage promotions and a terror aura, in exchange for reduced base ranged combat strength. Its availability at Education not only reflects how Greek Fire was a genuine (and genius) invention of the empire, but also synergizes with the civ's focus on specialists and allows the civ's power spike to be relevant on land and on the seas at the same time (I do find that, in this particular case, the two powerspikes don't stack too much, since they are on different parts of the battlefield and on units with quite different roles).
- Byzantium UB (Tetraconch) : In addition to providing the necessary faith to really push the civ into overdrive and scale throughout the game, I wanted to focus the building more on the theme of defensive scaling and helping the Capital. This Great Musician bonus, although a bit clunky I admit, is meant to provide this "wide specialist helping tall" strategy we dreamt about with pineappledan some time ago within a kit for which it totally makes sense.
So, that's all. As always, don't hesitate to express your opinions on the various ideas, and thanks for reading.
Edit 1 : Removed the Barbarian Encampment clearing bonus from Byzantium UA (too random) ; change the Tetraconch for the Hippodromos, and move the TRoute bonus of the building to the Arabian Suq ; limited the science + defense bonus of the Dar al-Shifa to +15% and +5 respectively ; added tech bonuses to the Aplekton.
Edit 2 : Replaced Faith with Gold in the Byzantine UA. Replaces Splash Damage I & II by a plague effect for the Dromon that increases flat damages received for afflicted enemies. Replaces the GP effect of the Hippodrome by a converter of Culture into Food (allowing the Byzantine capital to sustain itself from its cultural fame alone if used well). Changed Baghlah's free promotion from Skirmisher Doctrine to Pincer and reduced its base CS to compensate (ignore ZOC + movement after attack can be vicious) based on
@azum4roll's review.
Faith purchase costs,
Great People starting in the Classical Era.
Historic Event, gain +1 
Science, 
Culture and 
Gold in the 
Capital.
(+2) 16 
(+2)
Production cost
Food
Trade Routes coming to / from the City
Happiness
Citizens in the City
Unhappiness from Poverty in the City
GW Music slot
Moves restored to 4 (same as base knight)
