Answer
$cis-$1,2-dichlorocyclobutane has the higher molecular dipole moment.
Work Step by Step
In $cis-$1,2-dichlorocyclobutane, the two $C-Cl$ bonds are polar and their dipole moments are in the same direction, leading to a high molecular dipole moment. But in $trans-$1,3-dichlorocyclobutane, the dipole moments due to the polar $C-Cl$ bonds are in the opposite directions and cancel out, so the effective dipole moment of the molecule is zero. So,$cis-$1,2-dichlorocyclobutane has the higher molecular dipole moment.