Both are great computers. There are pros and cons to each. I would say it really comes down to how you plan to use it. If you plan to use it daily as a smart watch, the Garmin gets the nod. If you plan to only use it as a dive computer, it depends.
The Peregrine gets points for the color display, the G1 for GPS capability. I might give a slight edge to the Peregrine for the UI, but it’s slight. The Garmin UI is not bad at all, and like the SW is configurable.
Both can have dive logs downloaded via Bluetooth, but with the Garmin, it will only work with Garmin apps. For using other apps, the cable is needed. Replacement cables seem relatively reasonable compared to some others.
Charging is via Qi on the Peregrine vs. Proprietary cable with the G1.
You really can’t go wrong with either. I’d say it really comes down to two things. If you want a smart/activity watch as well, get the Garmin. If not, and the color display is most important, get the Shearwater.