Hi Chris, good job with this one.
As Ben said, the main difference is the direction of your pick when you are playing this lesson. Lian uses strictly downstrokes and this makes the riffs sound more aggressive and accentuated, and it also helps to keep timing tighter. Your take is lacking those things and the main reason is the mix of downpicking with alternate picking.
About pinch harmonics, the problem is not related to mix, it's related to technique, where you pick and the angle used. You should give a look at this lesson:
http://www.guitarmasterclass.net/ls/Pinch-Harmonics-Workout/and contact me if you need more help.
Gab.-