I've been mainly using large pistol primers in my 40-60 and 40-65 rifles shooting only BP. I have  tried some large rifle primers such  as CCI LRP BR2,  Sellier & Bellot large rifle, Fiocchi LR, none seemed to work  as well as the large  pistol primers in either of my rifles.
My question is, what others might be worth a try ?
Mike.

John, with black powder?

Oneatatime breech seating and using Smokeless.
Here is the link to the primer specs. showing the depth difference between the large pistol and large rifle. 

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I've been using federal large pistol primers for a decade with BP and use a primer swage to make the primer pocket  to fit large pistol primers, works like a champ.

For match accuracy using black powder, Remington 2-1/2 large pistol, Federal large pistol match and CCI BRII are my top three and I have tested them all. CCI 200 large rifle are the same as the BRII's but I am told by Mike V., the machines are slowed down and extra care is used to make the BR-II's. I have found the CCI 200 work as well but I use the BR's just because I can.  If I only had the CCI-200's I would use them in this time of shortage.

I hear from other people they like other brands but the above three are far and away what I hear the best about from those other riflemen that can put their shots in the middle, which agrees with my experience.

A friend pitted the face of his Miller DeHaas breech block using pistol primers in rifle cases. 
He used light smokeless powder loads in a Schuetzen rifle but the shallower seated pistol primers slamming back against the new modern steel breech block caused major pitting. 
The breech block face ended up with a concave surface that had to be welded over and machined flat again.
It can also happen using BP (Shiloh Sharps insists you do not use pistol primers in their rifles) but it may take a few more shots to show as much damage.

In both my .40-60 Maynard and my .40-65 WCF I use Remington 9 1/2 M primers to reduce fouling. 
Remington primers have been shown to have a hotter and longer flash than the other primers - which helps reduce BP fouling.
The magnum primer works just like a duplex load (not allowed in the Silhouette competitions) to help eliminate unburned powder being left in the barrel. 
But when doing so I place a newspaper wad inside the case over the primer channel (to stop Black Powder packing into the channel). 
Packed BP in the channel acts like a fuse which changes ignition patterns between shots which then affects accuracy.

Testing trials showed group sizes were half the size whenever I used loads with the newspaper wad over the primer channel.

SSShooter wrote on Jul 10^th, 2021 at 1:50pm:


Last time there was a SHORTAGE of primers I went and got 10k of each large/small pistol/rifle.  Down to 3k of small rifle now.

I forgot to mention I also tried FED GM215M Large Magnum Rifle Match Primers as well as the ones mentioned.
With my CPA Stevens I seat the pistol primers through paper so they are flush with the base of the case as if I didn't I was getting occasional misfires, requiring a second hammer strike, I still do this out of habit with the Meacham 40-65 just out of habit as in the Meacham it may not really be required.
I have also tried using a disc of tracing inside the case over the flash channel in case powder was filling the channel and perhaps causing a sort of fuse effect, There was no difference that I could detect.
I will try my local gun shop for some of the primers suggested if they have them in stock, and then report back.
Mike.   
Thanks again for all the suggestions, as they say here, you never know till you give it a go.