Quality wise there is no difference but should someone say that
FUNCTIONALLY there is none, they are either lying or inexperienced as a reloader.
There is a thing called brisance. Federals, the standard type in any size, have the lowest rating according to my testing. Here is how I did this: I took the exact same load, same day, same firearm, different primer and ran them over the chronograph. I used Federal, Winchester & Wolfe. It is common knowledge that CCI primers are the hardest to ignite so I NEVER buy them.
Then, I did two tests over the chronograph, 6 rounds single action, 6 rounds double action.
What I found out was amazing. (p.s. The gun was my M625JM with an extended firing pin added.)
In all of the loads, oh and by the way, these were target loads with either Bullseye or AA#2 as a propellant, the single action loads produced more velocity and better consistency than those run in the double action mode. Beside the point, I know, but may be useful information for someone at sometime!
The Federal primers have always gone off in the M625JM, the Winchester and Wolfe, not so much UNTIL I put the extended firing pin in and put a spent primer under the strain screw (a trick I learned from Joni-Lynn, here on this forum). Now all of them go off no matter how they are fired in the gun.
If you look at the spring kit offered as an after market kit from Brownell's for the "N" frame Smith with Jerry's name attached to it, it specifies Federal primers only after installation. Why would they do that if there was no functional difference? Exactly, there is.
Federal primers are easy to ignite and work exceptionally well in tuned actions. The Winchester gave much more consistent numbers across the chronograph even with these fast pistol powders. The Wolfe, they gave the same ballistic results as the Federal primers but acted like Winchester ones on how hard they were to ignite.
In another comparison, I used Wolfe Magnum Large pistol primers against the Winchester Large pistol that are rated for either. I found no functional difference in magnum loads using either. I used a M629 Classic in 5" barrel for that test.
In magnum loads, I only use Winchester Large or Wolfe Large and have never had any primer flow with either. I did have a bit of a problem when using Federal primers when we were doing testing for "THE LOAD". As pressures increased, they flowed and flattened out much sooner than the Wolfe ones I used for later testing.
While I am no expert, I do have a bit of experience in this one small area gathered through my own tests.
Of course, your mileage may vary!
Oh, and by the way, there is another area where they are quite different, price. As has been stated, Widener's has Wolfe primers for $15-$18/1000, CCI and Federal are both higher.