I recommend calculating the correlation coefficient; the correlation coefficient will directly tell you how much B is (linearly) different from A, and you can compute the SNR in dB from the correlation coefficient $\rho$ using
$$SNR = 10log_{10}\left(\frac{\rho^2}{1-\rho^2}\right)$$
Given you have a noise-free version of your waveform, this would be a perfect application for the approach above. In this case "noise" is any deviation from your noise-free waveform once the two signals are properly scaled (which the computation will do).
See this similar post where I detail the correlation coefficient calculation:
Noise detection