Most of the time you will be using PV=nRT to compare two gases.
P(delta)V is dealing with the expansion and compression of gases under different circumstances and how energy is affected.
Delta(V) is the change in volume so you would have to find out what your "new" volume is to use PV=nRT. Also P is the external pressure, not the internal pressure. You would need to know internal pressure as well.
P,V and T are state variables. Work(W) is not. That means that from state 1(p1,v1,t1) you can get to state 2(p2,v2,t2) with different amount of work. Transfer of heat will (or entropy) will spoil the picture