I have two different 10mm pistols and one Coonan Classic. (though it seems a misnomer, the "Classic" is the newly built and currently produced Coonan pistol)
Sticking to your stated intentions for this discussion (not being an argument between the two rounds and how they compare), I do wonder if it makes sense to at least address the differences when it comes to the handloader's point of view.
I'm a long time handloader of both rounds, and it makes for an interesting comparison if you are choosing between these two. Both are example of brass you simply don't often find scattered at a public range to be easily picked up and added to your cache of brass. 10mm rarely appears because it's not too popular and the folks who scatter it... chase it down. .357 rarely appears because most folks don't eject the stuff violently and lose it.
My Coonan runs
extremely well, but with two caveats:
--it does not like "wimpy" loads and you need to feed it full-bore, strong ammo that runs to the MAX load end. No middle of the road "Unique-powered" kinds of loads will run this pistol. AA#9, 2400, Power Pro 300-MP and the obvious one (that I have not used...) H110/W296 are the powders that
will run a Coonan properly. No handloads built with Titegroup, Bullseye, AA#2 or the like is going to run a Coonan, at least with regards to the full spring & set up for .357 Magnum.
--my Coonan scatters brass in every possible direction with no consistency other than the fact that it is inconsistent. The pistol shows obvious evidence that brass hits the slide as a normal part of the process and this has it flinging in a full 360-degree circle. As for picking up .357 brass, it's annoying, to be sure.
My 10mm pistols on the other hand will readily accept the full "range" of 10mm... most of the big name factory ammo is simply -NOT- built to the SAAMI potential of the round, by my handloads run from middle of the road (beyond the light factory) to full-bore, but still within SAAMI spec. It's also been my experience that every 10mm pistol I've worked with very much LOVES to launch brass in to the stratosphere. Some pistols are crazily consistent (my Glock 29!) and some are not, but all of them send the brass half the distance of the bullet, it seems.
Bottom line from a handloader's standpoint:
The Coonan that chucks .357 brass is easier to deal with when it comes to brass than the 10mm pistols are. Brass is more plentiful and (somewhat?) easier to find when you shoot the handgun.
I'd also submit that coming in to used .357 brass and purchasing bulk blasting component slugs is a lower-cost affair for .357 Magnum than for 10mm shooting, but YMMV.
If there is a "WILDCARD" bit to add that really hammers home my suggestion of a Coonan for you, it's that I have had
big time success in developing a
hot .38 Special load that runs the Coonan perfectly well with its
included 10-lb accessory spring. 125 or 130gr bullet in .38 Special brass running a load that I cannot post because it just barely eclipses all published loads with that powder. It runs the slugs just over 1,050 FPS and it makes the Coonan sing, all without the boom, blast, and BRASS of .357 Magnum. FWIW, I built this load because my gun club does not want the steel plates to be hammered with magnum loads, and I wanted to stay within their wishes. Shooting this load with the lighter spring is -NOT- the full "Coonan Experience" but it's a royal help of fun!
My Coonan has digested over 2,500 rounds of ammo since new, but I bet that roughly 1600-1800 of that has been my hot .38 Special load with the accessory 10-lb spring.