The first season is nearly identical; the only exception being the last episode (maybe the last two, I forget) which adds some Karasuma silliness.
Meanwhile, the second season is not so faithful. Filler is added to many episodes, and a couple of episodes are entirely made-up. Then, the last few episodes have a bunch of Yakumo and Tenma stuff that didn't happen in the manga counterparts. Strangely, some of the new developments at the end of the second season (like Tenma becoming Harima's manga assistant) not present in the respective manga chapter do happen much later--well after the anime aired.
Anyways, you can pick off where the anime left off. Start around Chapter 150 or 160.
Whoever fights monsters should see to it that in the process he does not become a monster. And if you gaze long enough into an abyss, the abyss will gaze back into you. - Friedrich Nietzsche