This would be close.
I think Kaine is a slightly superior politician. He has won statewide office three times, winning the bigger races by better margins than Kasich in Ohio in 2010. Republicans need to win Ohio, while Democrats can afford to lose Virginia.
Kaine's weakness is that Democrats have held the White House for the last two terms. As a Senator/ former DNC chair, he can't exactly run as an outsider.
I'd give Kasich the edge due to the tendency of parties to do worse in the third term.
Kasich/ Martinez- 282 Electoral Votes
Kaine/ Klobuchar- 256 Electoral Votes