My understanding is that the .500S&W was originally designed for 50,000 psi and used large pistol primers. Someone got the idea to qualify it for 60,000 psi. That required large rifle primers to avoid primer flow into the firing pin hole in the recoil shield. Early .500 S&W brass was cut for LP primers. A changeover was made relatively soon after things got started to LR primers. The LR primers are the same diameter, but a little greater height, so LP primers in primer pockets for LR will be a little low and could cause misfires. LR primers in LP primer pockets could be a little high and cause hangups of the cylinder.
I have Starline brass with LR pockets. If your Winchester brass is fairly recent, it should be cut for LR primers. You can try seating a LR primer in an empty case and see how well it seats. I use Federal 210 LR primers in mine (I think. I am at work at the moment.)