There is no date on when the claim was for or when it was made, so it is impossible to know if the Obama percentage is correct at whatever time its author made them.
But based on the entire two terms of both presidents and according to Cleveland.com:
George W. Bush spent some part of 1,020 days away (35%), including 149 days at Camp David.
Obama spent some part of 328 days away (11%), including 93 days at Camp David.
This is around the same amount as claimed for Bush, but more than twice the number claimed for Obama. However, the central point of Obama's vacation length being less holds true.
A couple additional points:
First, as CBS White House correspondent Mark Knoller says,
But a President is never really on "vacation." The job and responsibilities go with him wherever he is.
Unlike legislators, the President must be available 24/7 for security or or other urgent matters. Since "work on the road" is essentially a job requirement, it's hard to say what part of the President's time are spend working vs vacationing.
Second, as Politifact points out, the "vacation" patterns of Bush and Obama were very different since Bush owned a secondary residence in Texas which accounted for a large part of his "vacation" days.
Obama doesn’t own a vacation home, unlike Bush, who owned his ranch. So while Bush essentially used the ranch as as a working White House, Obama has traveled to a variety of destinations
EDIT: There is a additional suggestion by the image that conservatives call Obama "vacationer in chief". That was done by at least the Washington Examiner.