quantum field theory - Cross Section Peskin vs Srednicki

in Peskin Schroeder after the derivation of the differential cross section there is a comment for the central mass system (CMS), which says:

In the special case, where all four particles have identical masses (...), this [the general formula] reduces to the formula[...] (p.107):

$$\left(\frac{d\sigma}{d\Omega}\right)_{CM}=\frac{\left|\mathcal{M}\right|^2}{64\pi^2E_{CM}^2}$$ However in Srednicki the general formula for the differential cross section in the CMS is (p.97): $$\left(\frac{d\sigma}{d\Omega}\right)_{CM}=\frac{\left|\mathcal{M}\right|^2}{64\pi^2E_{CM}^2}\frac{\left|\textbf{k}^\prime\right|}{\left|\textbf{k}\right|}$$ where $\left|\textbf{k}^\prime\right|$ is the outgoing three-momentum in the CMS and $\left|\textbf{k}\right|$ the incoming. Now to get from the formula from Srednicki to Peskin's formula I don't need the masses to be all the same but merely the incoming masses equal to the outgoing masses, so to say elastic scattering. I didn't see a further restriction in Srednicki's formula apart from being in the CMS.

If I take e.g. Compton scattering I get with Srednicki's formula:

$$\left(\frac{d\sigma}{d\Omega}\right)_{CM}=\frac{\left|\mathcal{M}\right|^2}{64\pi^2E_{CM}^2}$$ but Peskin gets on page 164 with his formula for the differential cross section: $$\left(\frac{d\sigma}{d\Omega}\right)_{CM}=\frac{1}{32} \frac{1}{E_1E_2}\frac{\left|\textbf{k}^\prime\right|}{E_{CM}}$$ where $E_1+E_2=E_{CM}$.

I don't see, that this is equal? Is it actually equal? Where did I miss something?