Begovic had a dip mid season, the biggest issue being West Ham at home IIRC but generally he had a poor patch. Reportedly down to a niggly injury but regardless it was a dip all the same. One which Howe choose to play him through and out the other side of, rather than put Boruc back in. Something Howe has done in previous seasons for Boruc when he's had a dip in form / knock to his back etc.
However either side of that dip, Begovic has been consistent and fairly solid, and at his best has won us points on his own (like Boruc previously).
Any keeper is only as good as the defence in front of him and we all know that could be improved, but Begovic is decent enough and young enough to be our first choice keeper for several years to come. I hope / don't think there will be any change for a long time in our goal. There are certainly other players whom I would say have been poorer for us over the season.
I am surprised Boruc is happy to stay another year, but happy to have him so long as he's able to keep pushing the other keepers at the club.