Again, it was only running faster than that IN MENUS. AKA, the REALLY easy part to emulate. Watch the timer in the Melee fight. Shows who watched the video (and tried it on their own hardware).
Yes, the 400MHz difference is a factor, but not a 50% speed factor. The 3GB of RAM is irrelevant; Dolphin and Android combined don't use more than 1.5GB.
The fact that Galaxy Note 3 has Snapdragon 800 also makes a big difference. Think Intel Sandy Bridge vs Ivy Bridge CPUs. The Note's 3 Adreno 330 GPU is also about twice as powerful as the GS4's Adreno 320.
True it's not running perfectly, but it's pretty much guaranteed that the emulator won't run as well as on the GS4 compared to the Note 3.