"So long as your loads are developed with whatever primer you choose to use, you will be fine. Many people use "magnum" primers in standard type cartridges.
It likely is not necessary, but using magnum primers in a .270 is in no way dangerous, so long as proper load development procedures are used, not just subbing in a magnum primer for a standard one, without reducing the load and working back up."
Like he said.
The Federal and CCI standard primers are similar, except Federal cup is softer. The standard Wincester primer is hotter because it is intended for igniting ball powder.
Then the Federal and CCI Magnum primers are hotter still with the Winchester Magnum being similar or slightly hotter.
You can use any primer you want, in any application. If it works, it works.
But, if you use a standard CCI or Federal primer for ball powder, you can have ignition problems when conditions get a little worse - say softer strike in cold weather. Same problem if you don't use a Magnum primer for big cases full of slow powder. Might be just fine in the summer but a bummer in the fall and winter.
For non magnum and non ball applications, a hunter could buy some cold weather insurance by using the Winchester standard primer.
Magnum primers burn longer to improve ignition of heavily coated slow powders.
If you want to test primers, load a primed case and shoot it at a piece of paper 6" from the rifle muzzle. Do it in the dark and you will see the difference.