Buddhism, at its core, teaches that if you stop clinging to desire, suffering will cease.  Stoicism, at its core, teaches that inner peace is found by realizing what is in your control and can be changed, and what is outside of your control and can't be changed.

Clinging to desire is something that's within our control, and therefore can be changed.  Realizing this, the Stoics maintain, will lead to inner peace, and actually doing it, the Buddhists maintain, will bring about an end to suffering.

Of course, the actual letting go of desire is not as easy as it sounds, and when you realize that the goal of letting go of desire is itself actually just another desire, you'll find both Shakyamuni and Epictetus in agreement that you're finally starting to get it.