Bluetooth mouse lags, then has "delayed playback"
Check the Event Log for Bluetooth issues. Try to install the same driver version on both machines and see if the issue persists.
Bluetooth uses a wireless technology called FHSS (Frequency hopping spread spectrum), meaning any interference should be intermittent because it has the ability to "hop" frequencies. Bluetooth operates in the 2.4Ghz frequency if I recall correctly, so newer cordless phones and other wireless devices could cause intermittent interruption, although very brief.