At least for sufficiently large $N$, the case of equal masses reduces to the case of unequal masses to give a positive probability of bounded motion. This is because two bodies that are sufficiently close together relative to other masses can act as a body of twice the mass, since they will be energetically bound. Thus if one can build a solar system out of unequal masses, one can build a stable solar system out of equal masses.
Edit: Since two masses are stable, there is a positive probability of stability for any $N$ by iteratively replacing one mass by two.