It could become very interesting as it was the loss of Manzikert which not only lost the Empire pretty much all of Anatolia indefinately but caused the Byzantines to request aid from the Pope, eventually launching the Crusades.
But had the Byzantines won then it would probably not have made much of a difference to their fate in Anatolia. It was the loss not the battle itself which had such a powerful effect. It probably would have held back Seljuk control for probably another century at the most but I reckon by the end of the 12th Century Anatolia would still have been in Turkish hands. The Byzantines were just too corrupt which was really their Achilles Heel.
What could the world be like?
It could become very interesting as it was the loss of Manzikert which not only lost the Empire pretty much all of Anatolia indefinately but caused the Byzantines to request aid from the Pope, eventually launching the Crusades.
But I said eventually which meant more than a decade later.
I would have to disagree the Turkish conquest of Anatolia was actually the more unlikely outcome of the two. So many things had to go wrong for what happened to happen. First you had Isaac I giving up the throne because of an illness that turned out not to be fatal as was thought at the time. Then you had Isaac choose Constantine X who sadly was a piss poor Emperor over his own brother John who would have been a better candidate. Then after Constantine died Romanus Diogenes rebelled against his sons failed but not only was spared but end up as Emperor because Constantine’s widow Eudocia took a fancy to him. As you can imagine Romanus’ position was far from secure so how does he try to shore it up the tried and true method of starting a war. Sadly it was a war no one wanted Byzantium because Constantine had gutted the military so wasn’t in great shape to fight. Even the Seljuk’s didn’t want it because it came right as they were to about to try to take Syria. As far as the actually battle goes trajen777 did an excellent job of showing just how much the Byzantine’s had to screw the pooch in order to lose that fight.It's all moot of course since it depends on on success in several things, which makes it unlikey at best, ASB at worst. But if the Byzantines had not lost Anatolia in the first place, or regained it during the Crusading era, and not been dismembered in the 4th Crusade how would they have fared against the Mongols? I think the imperial army would be near a peak which usually came from a period of good government, and it would have the support of a strong centralised state by the time the mongols arrived.
The thing is though that they should have won the battle yes their military was nowhere near what it was during the reign of Basil II but they quite plausibly could have pulled off a win at Manzikert.I tend to think the empire was bound to get a serious defeat in the chaos between 1025 and 1081. 50+ years of internal problems is not conducive to an efficient armed forces, or a country which can withstand a defeat without losing half it's territory.
Personally if I was looking to have a stronger Byzantium with a POD around the time of Manzikert I would have had Isaac I not get ill and been succeeded by his brother John and then John’s son OTL Alexius I. With 3 strong military minded Emperors I think you could have the Empire sitting very pretty when the Seljuk collapse.The problem with the multitude of things which could have avoided Manzikert was that there was no major catalyst to galvanise the Byzantine leadership into action, Manzikert was that catalyst.
Anyway, perhaps Manizkert needn't be quite the disaster it was IOTL, even if it did need to happen. IOTL the Comnenos' regained control over the coast and the NW corner of Anatolia reasonably quickly, containing the Rum Sultanate to the rest of the Anatolian interior. So WI that was all the Seljuks took in the first place, and the Comnenos' came to power and began their revival holding the territory of 1150 instead of 1090? Would they be able to retake the entire plateau ITTL, and re-institue the Theme system properly?
As for your idea of having them lose Manzikert but avoid a lot of the nasty after effects it could be very interesting. The main thing would be to have Romanus killed either during or after the battle by Alp Arslan because a loss even a small one with his history would have made him keeping his throne very difficult. After that all you really need is a stable succession even leaving the idiot Michael Ducas on the throne would be fine since the bureaucracy would be able to keep the empire running ok if not particularly great. The sad fact of the Empire loosing Anatolia was almost as much due to the various factions inviting in the Turks in as support against the other factions as was the result of the Turks looking to annex land.
Draco
I remember reading that the crucial problem was not the defeat itself, which saw relatively little military losses but the civil war that followed and destroyed much of the armed strength of the empire. Think the same source mentioned that the far less defensible area in northern Syria actually held out against the Turks for several years simply because there were local Armenian forces stationed there to defend it.