Question: Let's consider 2 cases. First where a system is taken from state 1 to 2 in a reversible path. Second where the same system is taken from state 1 to 2 in an irreversible path. Can we say that Entropy change in both the cases will be same. 
This question is more like an extended version of this question [here](https://physics.stackexchange.com/q/540524/)

Answer: 
Yes! That is what you exactly mean by a [**state function**](https://en.m.wikipedia.org/wiki/State_function). The value of a state function does not depend on the path and process, it only depends on the state of the system which is completely defined by $n$ (number of moles), $P$ (Pressure), $V$ (Volume) and $T$ (Temperature). Thus the entropy change will remain the same regardless of the type of process.
To complement the other answers: the change in entropy of the *system* will be the same in both cases, but that of the *environment* will generally not.

If you split $\Delta S\_\mathrm{tot} = \Delta S\_\mathrm{sys} + \Delta S\_\mathrm{env}$, then the second law says $\Delta S\_\mathrm{tot} \geq 0$, with $=$ for reversible process and $>$ for irreversible processes. As $\Delta S\_\mathrm{sys} = S\_2 - S\_1$ is the same in both cases, you can infer:

* Reversible: $\Delta S\_\mathrm{env,rev} = -\Delta S\_\mathrm{sys}$
* Irreversible: $\Delta S\_\mathrm{env,irrev} > -\Delta S\_\mathrm{sys}$