I don’t think the Rehnquist comparison has much substance, regardless of who’s trying to employ it. In the case of Kagan v. Rehnquist, she comes out on top, not even close.

KAGAN:
1986-87: Clerk for Judge Abner Mikva, U.S. Court of Appeals, D.C. Circuit
1987-88: Clerk for Justice Thurgood Marshall, U.S. Supreme Court
1989-91: Associate in Private Practice, Williams & Connolly
1991-97: Assistant Professor and Professor, University of Chicago Law School (1991-94 as assistant professor)
1995-96: Associate White House Counsel
1997-99: Deputy Assistant to the President, Domestic Policy Council
1999-01: Visiting Professor, Harvard Law School
2001-03: Professor, Harvard Law School
2003-09: Dean of Harvard Law School
2009-10: Solicitor General of the United States

REHNQUIST:
1952-1953: Clerk For Justice Robert Jackson
1953-1969: Private Practice in Phoenix, AZ
1969-1971: Assistant USAG, Office of Legal Counsel