Nope. Since kinetic energy is a scalar quantity and momentum is a vector quantity, direction is the important key to determine this question.
Kinetic energy=(1/2) x mass x speed^2
Momentum=mass x velocity
Assume that both objects have the same mass, since they have the same kinetic energies, they will have the same speed. However, if they are travelling in different directions, they will have different momentum as the direction of velocity (Which is part of the calculation of momentum) will be different.
For example, if the two objects travel in opposite direction, one will have velocity, v, while the other will have velocity of -v. so the momentum of one will be negative while the other will be positive.
Of course, if we assume that both objects have different mass, their momentum may be different since the value of velocity not be the same anymore.