  In preparation for future space-borne gravitational-wave (GW) detectors,
should the modelling effort focus on high-precision vacuum templates or on the
astrophysical environment of the sources? We perform a systematic comparison of
the phase contributions caused by 1) known environmental effects in both
gaseous and stellar matter backgrounds, or 2) high-order post-Newtonian {(PN)}
terms in the evolution of mHz GW sources {during the inspiral stage of massive
binaries}. We use the accuracy of currently available analytical waveform
models as a benchmark {value, finding} the following trends: the largest
unmodelled phase contributions are likely environmental rather than PN for
binaries lighter than $\sim 10^7/(1+z)^2$~M$_{\odot}$, where $z$ is the
redshift. Binaries heavier than $\sim 10^8/(1+z)$~M$_{\odot}$ do not require
more accurate {inspiral} waveforms due to low signal-to-noise ratios (SNRs).
For high-SNR sources, environmental {phase contributions} are relevant at low
redshift, while high-order vacuum templates are required at $z > 4$. Led by
these findings, we argue that including environmental effects in waveform
models should be prioritised in order to maximize the science yield of future
mHz detectors.
