I'd say it wouldn't be much different.
Though Alexandria itself was a great learning center, the greatest hurdle to scientific advance seems to be the diffusion of knowledge, not only because it makes knowledge resilient to political shocks -- you can put only so many scholars in a single place, and when you're done there's always an asshole to burn it down, like Genghis did in Baghdad -- but also because it reaches out more people to do science work, and eventually it seeps into daily life. So even if the Library had survived, it might have just become an insular institution, like an Irish monastery during the Dark Ages. Until the invention, or introduction, of the printing press in the West, knowledge was easily lost, and not easily applicable to life.
On the other hand, if they could have managed to maintain papyri up to the 19th century, doing history of philosophy would be much easier.