@Lilith Thanks for reaching out!
This is a question that comes up often where I live in Fairbanks, Alaska and the short answer is that there really isn't going to be too much difference in the warmth of these two jackets. They are very comparable in length and insulation. The main difference between the two is that the Patagonia Tres 3-in-1 Parka gives you a little more versatility in varying temperatures and conditions. You can remove the liner and hood if you would like to, whereas the Arc'teryx Patera Insulated Parka does not have those options. Either way you go they're great parkas!
I hope this helps, thanks!