There is a school of thought that says whatever was there would have been suppressed by the Catholic Church anyway. (I read a book last week that said the great library was burned at the order of an archbishop who was later made a saint. But I have been unable to find any corroboration on this.)
There is no doubt that the amount of knowledge lost was tragic and set back the technological development of mankind hundreds of years. For example, the Minoans had harnessed geothermal energy and had hot and cold running water and showers in their homes on Thera. This was 400 years before the seige of Troy.
If the library's contents had not been destroyed, it is conceivable that the technology we have today could have existed at the time of Napoleon. The dark ages may have been a time of growing enlightenment, and the Plato ideal of republican government could have displaced monarchies centuries earlier than it actually happened. Knowledge of mediciine could have advanced to a point where the black death of the 14th century may have been much less severe. Settling of the Americas at the time of Charlemagne could have prevented the wholesale slaughter of the American Indians by the Spaniards.
However, the character of man is what it is, and we should not asssume that we would be living in a world of harmony and peace. Not all technology has been used in constructive ways, right? How would the world have been if Attilla the Hun had tanks and battleships?
Anyway, my opinion is that you could move us forward two to three hundred years. Colonies on Mars. Life spans approaching 200 years. Food enough to feed the planet.
It's all speculation, of course. Catherine the Great with nuclear weapons? We may not even exist today.