The main reason why the Turks poured into Asia Minor so easily was due to the Byzantine aristocracy's decision to turn the area into a massive sheep herding pasture. This meant that the Byzantines often hired Turks and Turks could easily settle and make their presence permanent following a capture of the territory. So, if the Byzantine aristocracy had not done this, the seminomadic pastoral turks wouldn't have conquered the region as easily as they did.
And the Byzantine state still carried lots of baggage from the Roman empire (in fact it was the same regime more or less). This includes the fact that everyone knows that real power in the Roman state was in the hands of anyone who could bribe or sway enough soldiers to support his bid for power. Also, the byzantine empire still ruled over multiple nations and even the Greeks weren't united. These peoples had little loyalty toward Constantinople and could rebel or be bought by pretenders to fight for them. The byzantine empire wasn't a "nation state" it was a state without a nation ruling over a myriad of cultures.
This made the Ottoman Empire much stronger. It was, more or less, a "nation state" with a strong relatively united Turkish nation at its heart. The Ottomans also learned a lot from the Byzantines and their failures (and successes). e.g. they went to great lengths to establish a stable government with a loyal soldier class who could not be easily bought by pretenders.
If the byzantine empire had survived, say ruling over Greece + modern turkey, I don't think it would have made much difference over how Europe developed. The Balkans might not have suffered the consequences of the Ottoman-Austrian/Hungarian wars, obviously and Albania would not be Muslim. But its perfectly possible, likely in fact, that Vienna and Constantinople would still have fought over the Balkans and many nations between them would have suffered. Byzantines did in fact have a record of ethnic cleansing, religious repression, thumb mutilation of their their victims, and all sort of predatory subjugation in general. In the end, north Europe would have industrialized, America would have been found, and history probably wouldn't have radically shifted. Constantinople would have felt the impoverishment of the Mediterranean just as the Ottomans did, perhaps even worse.