As you can see in the video below, when it comes to general benchmark tests, the results of the two Snapdragon 801-laden handsets are actually comparable with the Note 3. Granted, the Galaxy S5 outscores the rest of the quintet most of the time, but its difference with the One (M8) and Note 3 is not that large, and in the Vellamo browser test it even scored unimpressively.
When it comes to pure graphics prowess, however, the Adreno 330 GPU in Snapdragon 801 is clocked almost 30% higher than the same GPU in Snapdragon 800, with the respective gain in performance. In the T-Rex Offscreen test the One (M8) and Galaxy S5 outscored the Note 3 and the rest by a significant margin, precisely on account of the faster graphics chip.
In the end, all handsets, with the exception of the Nexus 5, performed very well, and the Note 3 held its own against the S5 and One (M8) in the general benchmark tests. When it comes to graphics rendering, however, the new Snapdragon 801 will clearly give you an edge in heavy 3D gaming, if that's your thing.