Answer
The B-Cl bond is more polar.
For B-Cl: Boron receives the partial positive charge, and chlorine receives the partial negative one.
For B-H: Boron receives the partial positive charge, and hydrogen receives the partial negative one.
Work Step by Step
According to the picture 6.8 (Page 263), the difference between the electronegativity of boron and chlorine (2.7 - 1.9 = 0.8) is greater than the same for boron and hydrogen (2.4 - 2.1 = 0.3).
Since that difference is proportional to the polarity of the bond, the B-Cl will be the more polar one.
For B-H: The less electronegative one is boron, so it will be the partial positive atom, and hydrogen will be the partial negative.
For B-Cl: The less electronegative one is boron, so it will be the partial positive atom, and chlorine will be the partial negative.
