I used Latigo (as my Dad got me started on them) from the mid seventies until I inherited a couple of rifles from my Dad several years ago when he passed, with Murray adjustable slings. I see no reason to change out the rifles that have Latigos already on them as they are great slings. However, when I got my Winchester Model 70 Featherweight 25-05 a few months back, I equipped it with a Murray.
As a side note, when I called the Murray number, the owner answered the phone. After speaking a few minutes and telling of how I found my way to them, we figured out that he was the brother of one of my Dad's good buddies. We had a good laugh and he told me some pretty cool stories about Dad and how much he liked him.
Edit to add, they have some really nice leather goods other than rifle slings at Murray.