The Resolution Glass Break Sensors come with 2 drywall anchors and 2 screws as well as 4 adhesive squares. Are the adhesive squares for something other than mounting? I have glass break sensors falling off of my walls throughout my house since I used the adhesive squares lol.
I will be using the screws but wanted to share with the rest of the you 
You can mount either way. Screws will definitely longer (pretty much forever) but double sided tape can last a very long time if done properly and mounted to a good clean surface of a material that works well with tape. I recommend wiping the surface with rubbing alcohol first to clean off any dirt and then letting it thoroughly dry before mounting. I can’t speak for the squares that come with Resolution Products sensors specifically because when we install we keep a roll of double sided tape from the hardware store in our toolboxes and I don’t keep track of which tape I’ve used but I would assume the squares they provide should work.
I bought some of my own after that and was thinking of trying it. The stuff that came with the sensors isn’t the best
I cleaned the wall and it doesn’t stick to either the wall or the sensor.
Typically the tape packaged with the sensors is going to be just strong enough to hold the sensor for a while under optimal clean conditions, but no stronger, so it’s not uncommon to see a piece that falls after a while. Perhaps the manufacturer doesn’t want to assume blame for paint chipped up from removal of stronger tape? Regardless it is best to use your own.
I personally just use the 3M outdoor double-sided mounting tape. You can use the “extreme” kind but it’s a bit more expensive and totally unnecessary for most sensors.