Both the HTC One Max and Samsung Galaxy Note 3 can record 1080p @ 30fps videos - the gold standard. The One Max throws in 720p @ 60fps but the Galaxy Note 3 tops it easily with 1080p @ 60fps, not to mention that it's one of the first phones that can record 2160p @ 30fps.
The HTC One Max records 1080p @ 30fps videos at a very good 21Mbps bitrate with 192Kbps audio bitrate (48kHz sampling rate). The Galaxy Note 3 uses lower bitrates on both counts - 17Mbps total bitrate and 128kBps audio rate (48kHz). Both devices record stereo sound.
The HTC One Max camera once again has the wider FoV, which again works a little bit against it when it comes to fine detail.
The end results are strongly in favor of the Samsung Galaxy Note 3. Even in the 1080p @ 30fps mode, the Note 3 manages to capture more detail than the One Max whose videos look too soft for FullHD. Then, of course, the Note 3 pulls the 2160p ace and completely trumps the One Max's video quality. Note that bitrate climbs up to almost 50Mbps, so 2160p videos can eat up your storage pretty quickly.
But it's worth it - 2160p is 3840 x 2160, while the resolution of the One Max for stills is 2688 x 1520. That means you can grab a frame from a 2160p video and have double the resolution of an HTC One Max photo.
Color rendering on either isn't particularly accurate, but the Note 3 has a slight advantage. The One Max also overexposes the shot, perhaps due to the narrower dynamic range we saw in the still camera. We do have one criticism for the Galaxy Note 3 and it's that the continuous autofocus triggered a bit too often.
The Samsung Galaxy Note 3 has one very impressive feature - 4x zoom in 1080p mode. It's almost as good as that of the Nokia Lumia 1020 despite the Galaxy's sensor not having nearly as many pixels. Here's a video demo of the zoom.
Both phones have High Framerate (HFR) modes, but the Galaxy Note 3 does it at 1080p resolution, while the One Max has to drop to 720p. An odd thing we noticed is that the 720p @ 60fps videos from the One Max have a wider FoV than the 1080p @ 30fps.
Obviously the quality drops when you enable HFR. In the Note 3 videos you can see less detail and noticeable aliasing. Still, we kept the 1080p @ 30fps crops from the HTC One Max to see how it stacks up against the Note 3's 1080p @ 60fps.
The HTC One Max manages to resolve even less detail than before in no small part due to the lower resolution, but the end result just isn't a very good 720p clip. The Samsung Galaxy Note 3 quality has dropped compared to its 30fps mode, but it still retains more fine detail than HTC One Max's 1080 @ 30fps video, which is pretty impressive.
Winner: Samsung Galaxy Note 3. The Galaxy phablet convincingly beat its opponent in every test here. Add the higher-resolution HFR video plus great video zoom and you get one of the best camcorders around, in daylight at least.
The HTC One Max video recording prowess is just no match for the Note 3.