Let m be the mass and v is the velocity of the light object.
M be the mass and V is the velocity of the heavy object.
Since both have the same momentum
mv = MV
The kinetic energy of light object be
(K.E)l = 1/2 mv2
The kinetic energy of heavy object be
(K.E)h = 1/2 MV2
(K.E)l /(K.E)h = M/m
Since m <M
∴ (K.E)l > (K.E)h
The kinetic energy of two objects will be the same if their mass and momentum are the same. Among light and heavy bodies, the Heavy body has the highest momentum. When the momentum is equal light body has more kinetic energy.