**Update**: There's nothing obviously preventing (negative) energy from bleeding from a pair of close bodies to others, so this answer is wrong as stated.

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.