Ψ and Φ agree at low PN order, but the waveform phases are actually exp(-imΨ), not exp(-imΦ). The orbital phase Φ is used, which is appropriate for evolving the dynamics; however producing the waveforms requires transforming to Ψ. Unfortunately this transformation includes a gauge parameter. The difference between Ψ and Φ affects the waveform at 4PN order.
Ψ and Φ agree at low PN order, but the waveform phases are actually exp(-imΨ), not exp(-imΦ). The orbital phase Φ is used, which is appropriate for evolving the dynamics; however producing the waveforms requires transforming to Ψ. Unfortunately this transformation includes a gauge parameter. The difference between Ψ and Φ affects the waveform at 4PN order.