Here is my load for my 300 wby
Barnes TTSX 168 gr
Rl 22 86 gr

two different primers and 200 fps faster and extractor marks with the Federal primer (L) compared to the Winchester primer. I didn't notice the extractor marks until I actually blew a primer with the Federal load. I've never seen that much difference in pressure from just a primer switch. Is this to be expected or is this an anomaly? The load is 1 gr below max also.
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And different brass......

You appear to have 2 different brands of brass also, so I'm thinking all else is not equal, and it's not just a primer switch that made the difference.

Every Weatherby I own leaves extractor marks on the rim with factory ammo.

Yep. Redo one's test with consistent ammo. Change only one thing at a time.

yes, brass also. I meant to mention that also. still a bit baffled by the big difference.

In my experience, RP brass is as thick as it gets in my little world. More than likely a good bit thicker than the Hornady brass on the right....the thicker brass, all other things being equal, will generate higher pressures. Obviously, all things were not equal though, with the primer difference.

Thinking the difference in cases, as pointed out by Wink is the contributing factor.

Have you checked case capacity between the two by chance? I've noted in some cartridges, the FC brass can be thickish (reduced case capacity).