If two gasses are in thermal equilbrium, do their molecules have same amount of Kinetic energy?
Two bodies in thermal equilibrium are at the same temperature. See the Zeroth law of thermodynamics.
Temperature is a direct function of average molecular Kinetic energy - by definition. There is no dependence on anything else like degrees of freedom etc.
There are other forms of molecular thermal energy storage - rotation and vibration about molecular bonds as two examples - and the total amount of energy stored internally in a molecule does depend on the total number of degrees of freedom of the molecule. The sum of the translational kinetic energy and all these other stored energies is referred to as internal energy U. That is where the confusion above originates. The total internal energies of the two gasses can be very different even though their average translational kinetic energies and thus their temperatures are the same.
So, YES - the translational kinetic energies of the two gasses in thermal equilibrium with each other will be equal. If their molecular masses are different, their molecular speeds will also be different. Their internal energies may be very different.