While scalable cell-free massive MIMO (CF-mMIMO) shows advantages in static conditions, the impact of its changing serving access point (AP) set in a mobile network is not yet addressed. In this paper we first derive the CPU cluster and AP handover rates of scalable CF-mMIMO as exact numerical results and tight closed form approximations. We then use our closed form handover rate result to analyse the mobility-aware throughput. We compare the mobility-aware spectral efficiency (SE) of scalable CF-mMIMO against distributed MIMO with pure network- and UE-centric AP selection, for different AP densities and handover delays. Our results reveal an important trade-off for future dense networks with low control delay: under moderate to high mobility, scalable CF-mMIMO maintains its advantage for the 95th-percentile users but at the cost of degraded median SE.