while i agree that note 2 sounded better than note 3, it didnt do so out of the box.
i had a custom firmware with a custom kernel supporting direct control and optimization for the wolfson dac in exyos note 2.
out of the box note 2 sounded lame.
note 3 snapdragon version isnt as good as custom kernel note 2 but with a lot of playing around with equalizer it does sound good (not great though)
i should point out that i have 9 IEMs and 7 full size cans including he400 hd650 and LCD 2 (version 1) with a few fiio amps/dacs and one top end burson audio dac/amp combo, so my views might be biased.
to the OP:
root your phone and install this:
forum.xda-developers.com/showthread.php?t=2470890 (for snapdragon sm-n9005 only, exynos has a different version)
i recommend the moderate version. the audio will be plenty loud enough and speaker will be very loud as well