If the needle is good and the record is new the LP has a better theoretical dynamic range - new record is important here as each time you play the record you physically wear it, so after a few playing it will not be as good. This is the only one that is inherently better.
LPs are sold to "audiophiles", and often have a different mix. The CD will often be compressed until there is very little dynamic range. Even when the record is worn it can still be much better just because the mix on the CD wasn't good in the first place. This is the biggest advantage to LPs, but it should not be overlooked as it applies often.