If your sine tone is buried in noise, you can only extract its information (incl. phase) if you have a sufficiently long portion of it, in which case the Extract Single Tone Information.vi will do the best possible job (better than simple filtering!). The VI bases its calculation on the spectrum (FFT) of your signal and the resolution is therefore proportional with the signal length.
A (bandpass) filter would have to settle before returning reliable phase and the noise would probably still be a issue. But if you are using the same filter on both channels, the phase difference should be unaffected.
Can you post a VI with your signals (a sufficient portion of it)?