Making it a single choice here made it tricky for me, but its a good exercise anyway.....
My criteria was this:
- Consequences of the battle (either short-term or long-term). Including whether the effect of the battle is significant on 'religious' point of view in addition to 'political'.
- The "What-if", in case we reverse the outcome of a battle.
- Scale of the engagement.
After this I've shortlisted: Yarmuk, Qaddissiya, Ain Jalut, and Hattin
The way I see it....
Yarmuk, Qaddissiya and Ain Jalut ranked higher than Hattin in terms of consequences and the What-if....This is because Yarmuk opened the door for the whole area until Spain and completely knocked Byzatines out of the Levant. Qaddissiya was a key battle that eased the Arab situation at Nehawand and paved the way for Muslim conquest up to China.
I ranked Ain Jalut slightly lesser than Yarmuk and Qaddissiya...Although I agree with Temujin that a Mongol victory would mean an absolute no opposition in the Middle East. I've considered that "Cultural" factors of mixing with rich civilizations of the Middle East will drive the Mongols back and/or cause some fragmentation, besides the Mongols are far from their bases.
Based on scale......Yarmuk and Qaddissiya were larger engagements compared to Ain Jalut and Hattin....
That left me with Yarmuk and Qaddissiya.....and I favored Yarmuk because of:
- Yarmuk completely ended Byzantine presence while it took another 2 major battles in Jalula and Nehawand to completely wipe the Sassanids.
- Yarmuk was a larger military engagement than Qaddissiya.
- Yarmuk also was mentioned in the Quran, as a prophecy that Muslims will gain victory in "Surat Al-Roum" (i.e. Chapter of the Romans).
- Yarmuk was a necessary victory because the Levant held hight importance to the Muslims due to its location, religious sense (as it included one of the 3 holy sites for Muslims), and cultural reasons (as its people and heritage were assimilated to Arabia more than anywhere else).
Conquest of Constantinople was a great Muslim victory, its something I really admire....I even watched the movie "Fetih 1453" 4 times !!
.....The reason its not my top choice is its low "What-if". Suppose Ottomans had to break and return then it wouldn't be the end of the world for them, they were already surrounding the city and Byzantines were in a weaker state than prior periods of Muslim engagements. Sultan Mehmet Fatih was very young himself and highly motivated, and could've returned to besiege the city.