On a round per round basis, I don't think that is quite the case, but quantity of CF versus RF makes up the difference. Here is the math:
Bullets: $300/1000 = 0.30/shot
Brass: $0.75 each = 0.10/shot (7 reloads)
Powder: $25/lb, 30 grain = 0.11 shot
Primer: $50/1000 = 0.05 shot
Add that up without barrel life and you get $0.56/shot => $28.00/50 shots.
Barrel life on a PPC is about 2000 rounds max at $400/barrel best case so add 0.20 more
Now you have 0.76/shot => $38/50 shots. That's about 2x to 2.5x rimfire ammo. THE KILLER ON RIMFIRE IS HOW MANY SHOTS ARE MADE THOUGH. In the end, rimfire is much more expensive given the number of shots. I burn at least a box a target so about $75 per day on a 4 card match (lasts about 3 hours too). A centerfire match for one day (all day) is 10 targets at about 10 shots/target => 100 shots or about $56.
That is probably why I have two varmint rifles, one in 204 Ruger and the other in 222 Remington and no rifle in 6 PPC. When Russ Haydon built my BAT action 222 he assured me the Krieger barrel, with that cartridge would give me tens of thousands of rounds, rather than hundreds or merely thousands of rounds before any significant wear would make me want to change barrels. As a result, my cost figures are a bit less than with 6 PPC. I actually expect to die of old age, before I wear out my barrel.
I have 475 of pieces of 222 Rem brass that I bought when Russ Haydon was going out of business and several pounds of H 322 I bought for under $10 a pound in another sale, so my actual costs are quite a bit less than the following figures, which are based on research I did today for current retail prices at such on-line sellers as Champion Shooter Supply and Midway. These figures are based on the real world prices for the standard loads I use with my BAT rifle and my Ruger No. 1V in 222 Rem. I have not yet loaded for my 204 Ruger.
Berger 52 Grain FB Bullets @ $0.26 per round.
22.2 gr. of H 322 @ $.07 per round
Lapua Brass @ .05 per round
Rem 7 1/2 Primers @ .02 ea
That gives an estimated cost of $0.40 per round. Now all of those costs are retail, with the highest quality of off the shelf components. If I was to substitute lesser components, the cost drops quite a bit.
With my 204 Ruger, I bought 150 rounds of commercially loaded Fiocchi 34 gr. V-max. @ $0.75 a round. Once I shoot up that factory ammunition, I will have 150 pieces of reusable brass essentially for free. I assume I will get about 500 reloads before I will need any more 204 Ruger brass.
To give a fair comparison, you need to buy top quality rimfire varmint or competition ammunition such as Remington Premier Magnum Rimfire (HMR) 17 Grain Hornady V-Max, which is currently at $0.41 - $0.45 a round at Midway. Or you could compare it to Eley Tenex @ $0.40 a round or (at least) Eley Match @ 0.32 per round at Champion Shooter Supply.
But none of those rimfire rounds will give the sub 1/4" 100 yard five shot groups, I regularly get with my 222 Rem. hand loads. I am still working with that rifle to achieve 5-shot groups under .2". I am pretty close now at .211"
So to summarize: Though loading and shooting my BAT rifle with high quality components costs me about the same per round as firing rimfire rifles with similarly high quality components, the results with centerfire are in another universe from rimfire.
I confess to being a high volume shooter with rimfire and centerfire, though as you said there is a difference. A typical day at the range for me is 20-50 rounds of centerfire. while a day with rimfire is 100-200 rounds.
PS: Buying locally at Sportco a couple of years ago, I bought a few boxes of Federal Premium Gold Medal Match Rimfire Ammunition 922A to try it out. I was not paying attention to the price, as I checked out with that and a few other items. I got home and found I had paid the astounding price of over $20 a box. Perhaps that is why I currently buy all of my rimfire ammunition on-line,