Methods for deriving goldstone theorem

I am reading chapter 19 of Weinberg Vol. 2, and in section 19.2 he gives two proof of goldstone theorems – one uses functional method involving quantum effective action and other is operator method involving general arguments related to commutator of current and field, current conservation and Lorentz invariance (to restrict forms of spectral functions). My question is both these approaches implied that for broken global symmetries there will be massless particles, but in second method yields much more information like the massless particle should have spin-0 (helicity) and have same parity and quantum numbers as $J^{0}$ and I don’t see a way to derive these conclusions from functional methods.
Does that mean that operator method has much more information than functional method, and in general can we argue that operator quantization has much more information than path integral quantization?