PART IV—ARREST AND SURRENDER OF PERSONS TO ICC
Restrictions on Surrender
60.
(3) If Kenya is under an existing international obligation to extradite the person to the requesting State, the Minister shall determine whether to surrender the person to the ICC or to extradite the person to the requesting State.
(4) In making the determination under subsection (3), the Minister shall consider all the relevant factors, including those matters specified in section 59, but shall give special consideration to the relative seriousness of the offences for which surrender is sought.
Competing request - different conduct - international obligation to extradite
EDIT.