I used to own a Polar 825x and switched to an Edge 305 about 2 years ago.

Main difference on paper is GPS tracking allowing you to download your route to your computer and see it on a satellite map. It's not necessary but a fun tool, I like it a lot.
Secondary difference is support for the Mac, although Garmin software is not great. So if you are a Mac user both options will require a 3rd party software such as iSmartTrain for the Polar or Ascent for the Garmin. Ascent is really, really nice.

On practice I give a huge thumbs up to the Garmin for their HR belt, it's a lot more consistent than the Polar's that needed really good care and tended to require a replacement every year or so. The Edge also pick up much less interferences (from powerlines to cars) than the Polar. So I find the Edge to be more accurate and consistent.
Polar has an advantage on battery life, the Edge will track up to 8 hours unless you have an extension battery such as the MintyBoost kit or a retail charger such as the Energizer Energi To Go. The Garmin has a rechargeable battery while the Polar uses a button battery that needs to be replaced every couple of years, the Edge sensor need new batteries once a year.

You can upload crude maps in the 305, I have never done it but it is possible to do it with proper software.