As the owner of both a v650 and Garmin 1000, I have to say I prefer the Garmin. While the v650 will do mapping, it is not a functional GPS. Its navigation is fixed to routes preplanned and saved via the Polar web app ahead of time, with no ability to get you back on route, at least in my experience. I never relied on it for GPS for this reason, and I generally look over a map before deciding on a new route. I tote my phone in a bag in case I get in a pinch or lost.
The v650 only works with Bluetooth (BT) sensors, so that is something to consider. Initially I chose the v650 because of the lower price, and that I have an older, pre-BT model Polar Accurex HRM that lasted for years. In fact it still works, although the wrist strap is toast. I used a Polar H7 chest strap with it, and have to admit Polar still makes the best HRM chest units.
Unfortunately, the Garmin only uses ANT, which limits you to Garmin's chest strap or Wahoo's dual BT/ANT chest strap. I use the Wahoo HRM with the Garmin, and previously with the v650. Not fond of the strap itself, as it is easy to separate the two halves, but that's a minor nitpick. I also use the Wahoo Blue SC dual BT/ANT speed and cadence on my mountain bike, and a Bontrager BT/ANT unit on my commuter, and both work great with the Garmin. These same sensors were hit or miss with the Polar.
My main complaint with the Polar is that it continually dropped sensors, including Polar's own HRM, the H7. In daily use, it lost sensors more often than not. And it was never consistently one sensor. Coupled with the fact that Polar appears to have stopped adding features to it (no updates in months), especially with the newest, non-color model (4-something or other) to their lineup now offering some features lacking from what was supposed to be the top model, I just gave up and splurged on a Garmin.
I don't really need a fancy computer, (I don't race, I just like the data), but if I am going to use one, I want it to work. I read that the initial release of the 1000 was wonky, and the price scared me off, so I opted for the Polar. The Polar display is nice, the touch screen works, and the small light is actually useful as a small flashlight, I have to admit. For recording ride information when the stars (sensors) are aligned it works. But if it drops a sensor partway through your ride, forget it. I purchased the Garmin a few months ago, so it's a more mature product than the initial release, with at least three software updates since purchasing. I have yet to experience dropped sensors or crashes/freezes in daily use, so I don't regret the purchase. The display is nice, and it offers more GPS functionality than the Polar, such as genuine routing, although I have yet to use that function.
Another bonus to the Garmin is that it interfaces with Garmin cameras, including the older Virb Elite units that are now decently priced. I use these as safety cameras to record my eventual demise from an automobile, or Darwin Award moment. The 1000 will start the Virb recording with the ride. The Garmin Varia radar and lights will also work with it, as noted by others, although they are a bit pricey in my opinion.
The Hammerhead unit does look promising, especially with its introductory price, but time will tell if it delivers. The Wahoo units are worth a look, but not quite sure if they have full GPS routing.
Hope my comments help!