There is no easy answer to this question as success can be measured in many ways. However, if we look at their careers overall, Murali Vijay has been more successful than Dinesh Karthik.
Murali Vijay made his Test debut for India in 2008 and has since played 38 Test matches, scoring over 2,500 runs at an average of over 40. He has also made centuries in all three formats of the game and was part of the Indian team that won the 2011 World Cup.
Dinesh Karthik made his debut for India in 2004 and has played 23 Test matches, scoring just over 1,000 runs at an average of less than 30. He has only made one century in Test cricket and has never been part of an Indian World Cup-winning team.
So, if we look at their respective careers, Murali Vijay has been more successful than Dinesh Karthik.