My number one nemesis in high-end audio has always been "brightness", so I understand.
IMHO, the Canare will be a little more "polite" than the Mogami, but you'll need to try them for sure.
Balanced connections are usually cleaner, with less noise. That's the purpose for a true balanced connection, is to keep the noise out, especially on longer runs of cable.
Most audio systems use shorter cables lengths, so the difference is subtle, but can be impactful...