Ottoman ships werent inferior to european ones. The ottomans just used ship fit for the med because they didnt have direct accses to the atlantic or any other ocean for that matter so they didnt need the bigger european ships used to colonize the new world. And any power the ottomans faced in the med would also be using med orianted ships. It was latter on when the race for the new world got full under way or colonialism got full blown that the ottomans became increasingly inferior to european navies.
I'm afraid that the Ottoman ships were MUCH inferior to european ones, especially regarding heavy gun firepower (lack of), light gun firepower (consisting in prevalently in archers), open-sea voyages (unable of), signal lanterns (all bought from Venice).