Getting the pressure using the equation of states - will the answer be the same?
In general no, the pressure will not be the same, although there will be intersection points where (by coincidence) they will be the same, and there will be regions of the phase diagram for some equations of state (EOS) and for some substances that might be close enough that it doesn't matter.

For example, the van der Waals EOS gives pressure values at high temperature and low pressure for noble gases that are close to what you would obtain with the ideal gas law.

Since it is typically easy to calculate pressure from an EOS given temperature and volume, you can try this yourself and see how much of an impact the choice of EOS makes for your particular system at a particular point in phase-space.