These observations are based on the 2016 editions of these headsets. It's entirely possible that one or both companies will release radically different hardware in the new year, but going off their current trajectories, I'm Team Daydream for the following reasons.
Daydream's bundled controller trounces the Gear's touchpad
On the Gear VR, you're either swiping the touchpad built into the headset, or you're using a standard third-party gamepad. Neither input method reproduces VR gestures that mimic your real-world hand movements.
Daydream ships with a controller that doesn't look like much, but it contains an accelerometer and gyroscope – almost like a Nintendo Wii controller – so some of your real-life movements can be channeled through virtual reality. Compared to the Gear VR, it comes much closer to offering a hands-on feel. Don't expect it to rival Oculus Touch, since it does not have positional tracking, but at least the two feel (distantly) related.
We're still waiting for Daydream content that truly capitalizes on what the controllers are capable of, but there are a few titles that offer glimpses. For example, Fantastic Beasts and Where to Find Them is not a full-length adventure game, but it does have you brandishing the controller like a magic wand. It would be exciting to see a more sophisticated rendition of this kind of physical spell-casting.
Daydream is compatible with more smartphone brands
The consumer Gear VR was first introduced last year. It's only compatible with Samsung Galaxy S6 phones and newer (six phones in total)
There have not been official confirmations about which phones will be compatible next, but it's hard to imagine many manufacturers of high-end Android phones opting out of Google's certification. I expect that most of 2017's major Android flagships will work with Daydream.
Inserting the phone & firing up VR is easier on Daydream
The Gear VR plugs into the port at the bottom of your phone. Once it's snapped in, the top of the phone is held into place with another prong, meant to keep the phone mounted flush against the headset. You insert your phone while it's on the home screen, and the Gear VR library automatically fires up once it's mounted.
At least with my unit, the smaller Galaxy S6 does not fit into the Gear as perfectly as it's supposed to, and the auto-launch feature is inconsistent. But even if the Gear VR does fire up as intended, Daydream's lower-tech approach is still easier and more reliable: Open the VR game or app, then drop the phone into a trapdoor which bungees shut. The phone stays snug and secure no matter which weird movements your VR session prompts, with no USB port required.
The content library will continue to grow
The biggest count against the Daydream? Its content library is sorely lacking, but I expect that's largely due to its brand-new status. If the rapid growth of other Google platforms (including Google Cardboard) is any indication, Google's open platform will prompt Daydream content proliferation before too long.
Samsung does have help from Oculus – the VR company is dishing out heaps of money for developers to work off its platform – but it's unclear how much of those efforts are focused on Oculus Rift, and how long the content will remain Rift/Gear exclusives. Many top Gear VR titles have already showed up in the Daydream library.
Daydream is better looking
Daydream's soft, washable exterior and refreshing departure from hard black plastic makes it much more visually appealing than the Gear VR. External looks might seem like an afterthought to those who have already been on the inside of a VR headset, but I think that a more attractive headset is a boon to adoptability.
Many remaining issues are minor or easily remedied
Fit is also a major deciding factor in selecting any kind of headset. Many industry voices say that the Gear VR's big, spacious headset fits better than the Daydream, but in my experience the opposite is true. On my head, the too-wide Gear lets light in around the sides of my face, but the narrower Daydream lets in light around the nose. I expect that many other wearers are divided in fit preference as well.
Similar Daydream shortcomings – adjustability and degree of eyeglass compatibility – will constitute only minor bummers for most users.
Major shortcomings are true across mobile VR
No matter which headset you use, mobile VR's major limitations lay not with the headsets, but with the phones that power them. At this point, both the Gear and Daydream are subject to smartphone display quality and processing power. Headset differences are minor compared to the platform and hardware powering them.
Of course, this dynamic would change if either headset manufacturer makes dramatic technological improvements. Samsung/Oculus seem more likely to win this race: Oculus CTO John Carmack has referred to his own efforts to bring positional tracking to Gear VR, but there's no word on whether those efforts are coming to fruition. Positional tracking – that is, the ability to track your below-the-neck movement through space – would be a complete game changer. Gear VR would leave Daydream in the dust if it were to implement this exclusively.
On the other hand, Google has the obvious advantage in software platform development, and its release of the well-regarded Pixel phones suggest its growing potential in hardware manufacturing as well. Making 2017 predictions based on 2016 hardware, I expect that the Daydream will incrementally take over the top spot in mobile VR. There's a small chance the Oculus will pull out some big guns in a 2017 Gear VR update, but I think that's more likely further into the future.
For more info on the state of mobile VR:
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