Dear pnanda65675,
Of course you can do ac analysis and get the phase shift. But that would be confusing for you are making the notice in frequency domain. My idea was since you will be doing a transient analysis, you can take the value of the output of the two stages at any time, "t" and then do a Sine Inverse on them. Since, your wave function is A.Sin(ωt + Φ), and A, ω, t are common to both the waves, when you take the sine inverse function, the difference in each values give the phase shift.
I hope that I am clear.............