Pressure over a solution
If the vapor (i.e. gas) phase above the solution can be treated as an ideal gas, then yes, if two species have the same partial pressure, then they have the same mole fraction.

For an ideal gas mixture, $p_i = y_i P$, where $p_i$ is the partial pressure of species $i$ and $y_i$ is the mole fraction of $i$ in the vapor phase, and $P$ is the total pressure.

The ideal gas assumption will be very accurate in many cases commonly encountered in chemistry, but not always.  Binary mixtures of $\ce{CO2}$ and another compound at high pressure would be one example of vapor phases that are not ideal.  Concentrated vapor of aliphatic carboxylic acids is also not very ideal.