Ottomans are killer beasts. One guy showed that the Ottoman bonuses to manpower, morale, unit power, and discipline can allow them to beat Prussia or Sweden man-for-man. And that's without 300% manpower recovery... Your only hope to beat them is to try to outnumber them 2-1 in every battle. Westernizing can be a huge help, but if you westernize too soon then you'll be stuck with crappy units. Don't westernize until land 14 or whatever gets you Tercios.
Yeah, they are tough.
In my Mughals game, as detailed somewhat in a prior thread, I managed to avoid fighting them until about 1580, despite a common border. Some combination of luck and relative strength. They attacked me then and I had no hope - peaced them out for money.
Then I prematurely westernized - this around military tech 14 or 15 - and have now beaten them in 4 wars. The wars are getting progressively easier, though they are still tough. I don't need numerical advantages to beat them, at least fighting defensively, but take enormous casualties - which is why (recovering manpower) I've only been able to fight 4 wars against them and it's now around 1630.
My dilemma now is that further expansion into Anationalia is going to be brutal in terms of coring cost/time, as almost all of the non Ottoman cores are long gone (ai Ottomans tend to culture convert, which means even the non-expiring cores are gone). Options are Russia - though seeing how they trashed the Ottomans even with a numerical disadvantage makes me think that I am not ready for that - or, more likely, North Africa. I'm lucky there - Mameluke vassal, cheap Tripoli cores (owned still by the Ottomans), and Tunisia of all nations has blogged to wipe out Algeria and Morocco. I am pretty sure all of their cores remain, so I can play the release and feed game big time. AND since the Tunisians don't have Berber tradition, the little coring that I have to do should be fairly cheap.
One interesting thing in my game is that Russia, deprived of Siberia, didn't expand much during the 16th century. Finally they started expanding again around 1600, and have absorbed much of the horde lands to their south and my west. They even took some provinces in the Caucus, interfering a little with my expansion plans in that direction.