In my 6mm Creedmoors I've used Lapua (6.5 resized with LRP and 6mm with SRP), Peterson and Hornady Brass. I've used the 6.5 Creedmoor Nosler Brass in my 6.5 Creedmoor that I could easily resize to 6mm Creedmoor. In other cartridges I've used Remington, Norma, Winchester and many other brands of brass. They will all serve the purpose and with the current shortages I would buy whatever brand you can find at a reasonable price. I've yet to have any issues with the small rifle primers in cold weather but I don't think I've tried shooting them in below 0 temperatures yet. If you are often hunting in very cold temperatures, then I could see a reason to avoid small rifle primers but for most of us that is going to be a none issue. The advantage to the SRP is that the primer pockets will likely last longer. My 22-250 has ruined LRP pockets in less than 4 loads on cheaper brass, with Lapua LRP in my 22-250 I haven't had an issue with "loose" primer pockets after multiple hot loads.
Lapua brass has a solid history of quality and durability that all other brass are compared to. I have been very impressed with the Peterson brass. If my Peterson brass lasts as long as my Lapua brass, I would be buying Peterson brass as a 1st choice in the future because their packaging is superior. Every piece of Peterson brass that I've bought has been flawless. With new boxes of Lapua brass there are often a few pieces out of 100 that have been dented because it isn't packaged as well as Peterson.
With all that said, I recently ordered 500 Peterson 6mm Creedmoor SRP. If I could have found Lapua SRP for the same price, I would have been tempted to buy Lapua instead. Lapua quality is excellent but due to the way it is shipped, I often find myself doing at least a little prep work the first time I load it. The nice thing about the Peterson brass in the 50 boxes that I've ordered in the past took zero prep work before I load it for the first time. My bulk order of 500 does have a disclaimer that it is not packaged as well as the 50 boxes so I guess I'll find out if some of it has dents that requires resizing.
Peterson brass is also made in America. I'm also happy to support a good company like Lapua but it is good for us shooters to have multiple American made components from quality companies like Peterson, Hornaday, Nosler, etc.