Our usual caution here applies: you're watching this through the veil of Vimeo comparession, which is - with all respect to Vimeo - like looking at the Mona Lisa through a beer glass. But you can see a difference and it's quite significant in this case.
Leaves are difficult
It's worth mentioning that this test uses moving foliage as its subject, which is notoriously difficult to capture using Long-GOP codecs like AVCHD. So you do have to treat this as something of a worst possible case. But it's exactly this type of case where you might want to consider using an external recorder (an Atomos Ninja 2 in this case)
There's no criticism of Canon intended by pointing this out. It's actually a testament to the quality of the camera and lens that you can capture a significantly better image if you take the uncompressed feed out of the HDMI socket: all a recorder can do is capture whatever it is fed.