I voted weapons, but it is both that and the augments a card has that determines if I’ll use it. Empire-9 on Fletcher for instance I have to have due to how much better it is than his primary weapons. I also had to have a kukri knife on the two primary weapons of Redeye I use. In the case of say Phoenix, I have to have potent packs or his healing just seems mediocre.
How do you judge your loadout cards?
Weapon>perks>skin>rarity. The first 2 are really important because they influence gameplay, the other 2 (skin and rarity) have no influence at all so I don’t know why you would care as much for it. If a cobalt has a worse loadout than a Bronze then why would you use it? Just because it shinier doesn’t mean it’s better. (imo) 
By complete loadout (weapons + augments), then by skins. I don’t care if a card is rare if the skin looks stupid.
I mostly judge them by weapons. I prefer a specific primary, secondaries are fine in general, i get a machine pistol wherever i can, and i prefer beckhill knife over any other meelee weapon. Augments are important, but if i like a weapon combo i tend to prefer that over a good aug combo.
Weapons are the most important but really all of these are equally important.