What Turkey would gain, among others are,
a) The institutional framework : The most outstanding component of being a developed nation is to have the right functional institutions in place. Turkey today is richer than Germany 20 years ago, but still not as developed mostly because of the missing institutions. EU is not the procurer for such institutions but an effective catalyst in building them.
b) Economic Integration and Stability : Most of the economic and political crises in Turkey have happened due to Political and economic instability. The Integration with Europe will alleviate all that to a minimum. It will not totally eliminate since some things depend on domestic issues (such as the Greek, Spanish, other crisis in Europe) yet will benefit Turkey immensely.
c) Free movement of people. Integration requires free movement of labor, capital, goods and services. Only the labor cannot freely move currently, which effectively isolates Turkey from much of the world. The elimination or ease in such barriers will only benefit Turkey.
other reasons can be added...
Maybe the other half can see these reasons. Capital moves anyway, why couldn´t people move as well?
Going Europe doesn´t have to mean going there as the conqueror. There are good examples of fruitful cooperation in the history of Ottomans.