That makes perfect sense, actually. The battery saver mode most likely kills things like Bluetooth, wifi, apps, etc, that are running in the background, so that the musical signal path is "purer" and less noisy, which results in higher sound quality!
The HiBy R6Pro, as well as a few other DAP's, have a "music mode", that does the same thing, for better SQ. So it totally makes sense that the M11's "battery saver mode" has the best SQ, because it's most likely shutting down everything unnecessary for just listening to music, at least with a wired cable coming from the 2.5/3.5/4.4 outputs!!!
My Shanling Audio M5s DAP might be a mid-tier DAP, but it sounds heavenly right out of the box, without having to switch into a "music mode/battery saver"!!!
That said, I've been eyeing up the whole FiiO DAP lineup, to possibly replace my Sony NW-A35 Walkman as my car's Bluetooth source! I have a mint condition 2009 Lincoln MKZ, with an AMAZING sound system, so if anyone has any opinions for the FiiO DAP with the BEST Bluetooth sound, I'd greatly appreciate it!!!