Step 1: Bond order calculation.
Bond order of O$_2^+$ = 2.5 and bond order of N$_2^-$ = 2.5. Step 2: Magnetic nature.
Both species contain one unpaired electron, hence both are paramagnetic. Step 3: Conclusion.
Thus, O$_2^+$ and N$_2^-$ have same bond order and are paramagnetic.