CDs have far superior bass. CD can reproduce perfectly down to practically DC with its entire dynamic range. (It's not really DC since CD doesn't have infinite playtime, but 1/(60*80) Hz is DC for all practical purposes.) LP has mono bass, lots of bass distortion, and very limited bass dynamic range.
True, non-mono bass can throw the needle out of the groove, and a loud bass frequency will quash everything else.
Must of what people don't like about "digital sound" is actually just contemporary production/mastering techniques, esp. stupid, unnecessary compression, which studies have shown to fatigue people's hearing more quickly.