There are basically two factions of TEOTWAWKI survivalists, the primitives and the modern. The modern survivalist are in the majority, because no matter how many of them believe that primitive skills are all important, they are not willing to give themselves over wholly to being primitive. They want the best of both worlds, and in my opinion this will not work in the long run. You need to be one or the other.
Modern gear and firearms will give the modern survivalist an advantage in a violent urban environment. Even if they grow a brain & get out of the city to survive in the bush, the early days should be pleasantly comfortable. But further down the track, this modern gear will start to break down, clothing, equipment and arms will become useless. The modern firearm requires breech-loading ammunition, which in the larger calibers is bulky and heavy. Out bush there will be no gun shops to supply more ammo, so they will have to carry it all with them. When it is spent, or if the gun should malfunction, all they have left is a fancy club.
But it is not just the modern equipment that makes the difference, it is the way of thinking and the attitude that goes with it. When most of the modern equipment is gone, they will be thrown back into the stone age, but with a modern mind and experiences.
My opinion is that the primitives will be the long term survivors. The level of comfort early on will not be great, but, it will not ever change. Whatever they start off with, they will retain. IF there is to be any fighting later on, it will be done with bows, slings and hand to hand. The 18th century lifestyle or earlier is well suited to this, but the modern survivalists will be totally dependent on their so called short bladed survival knives and possibly the odd machete. Some will experiment with making bows and arrows and other primitive weapons, but the majority will have a hard time surviving.
18th century primitives will have the advantage of carrying muzzle-loading guns, rifles and pistols, plus knives, tomahawks and possibly even swords. Bows will be popular, self-bows, not compound bows. They will have attained the wilderness survival skills of hunting, trapping, making moccasins and much much more. They will not be the ones to get into fire fights, they will be keeping a low profile and leaving the cities to live permanently in the wilderness. The bush will be their domain, a place where they will have the advantage.