Short answer. S&W 500 Magnum and 960 JDJ have the most "stopping power" on average. I suggest you stick to 9mm and .308 because trust me.
Well from the information you've given me in your question I can come down to two main cartridges.
Pistol: .500 S&W magnum
Rifle: .50 BMG or .700 Nitro Express
Check the literature...there no units for or way of measuring "stopping power". It is a meaningless term without of context. What are we stopping? How may shots do we get? Who is doing the shooting? Are we talking statistically real word, where 50% of the shots don't even hit the person, or are we assuming a targeted center mass shoot.
ANY intermediate to full power rifle cartridge is highly likely stop someone with a center mass shot.
Taking in all factors, the FBI recently released a study that suggested that the best round their agents should carry is 9mm Luger. Shot placement is more important than the cartridge used.
9 mm parabellum is pretty impressive - which is probably why it's the most popular pistol cartridge in the world. The US army now uses that instead of the old .45 ACP.
But of course something like a .357 is heavier and hits harder - and then the .44 magnum hits harder yet.
As for rifle bullets, I've always liked the old .06 - goes off like a house a'fire.
Evan Marshall (retired Detroit cop with a physics back ground) and Ed Sandow wrote a book based on questionable methodology a few years back... "Stopping Power"
Based on there work the ranked handgun caliber and found that the .357 Magnum produced "one shot stops" about 60% of the time based on reported shootings (mostly police reports) and ER results... 45 ACP and 38 Special were not that far off compared to the popular 357 Mag.
Most folks in the last 30 years have been happy with the modern 9mmx19... 45 ACP.. 40 SW and 357 Sig.... that said 80% of handgun shootings require 2 hits to stop the assailant from pressing his attack
OK, for a pistol you want to hit with 300-580 foot pounds if you are a civilian, and 400-580 foot pounds if you are a policeman. Anything less won´t score you a knockdown. The police use 9mm [342], 40S&W [479], .357sig [502], 45ACP [369], and 10mm [680] because they understand that any more or less knockdown power won´t help them. It is a compromise between handling and knockdown power. Square velocity and multiply by bullet grains, then divide by 450240 to calculate foot pounds. Don´t shy away from light, fast, and explosively expanding ammo. A 22 long rifle will get you about 165 foot pounds. That´s more than a 100 mph fast ball. A 22 Magnum will get you about 350 foot pounds. Most other shotguns and rifles will get you up to 2000 foot pounds, and they are more accurate than handguns. Get the words ¨stopping-power¨ out of your vocabulary if you are not a policeman. Get a knock-down, and run away. Dead or alive, let the police take the gun out of the other guys hand.
To answer your question: 357 magnum revolver 624 ft pds, 45ACP semi-auto pistol 369 ft pds, 12 gauge slug, and .308 rifle 3600 ft pds, as evidenced in the book ¨Stopping Power¨ by Marshall and Sanow. Full size open carry pistols do much better than compact conceal/carry models.
JD Jones made a pistol with a 50cal BMG barrel on it I am told. This, would be the most powerful pistol on the planet. I am also told he has yet to find anyone sober who wants to fire it. Sometimes the biggest of anything - is also impractical.
The most powerful pistols and rifles - will also be the heaviest, hardest to conceal pistol, and, the heaviest and nearly impossible to carry rifle weighing 3x more than a regular rifle. The 50bmg rifle I once fired 18 years ago was 24 pounds........ a standard hunting rifle runs between 7 to 9 pounds.
Pistol - 500 S&W would be it. I have watched people fire this. They fire 1 round, swear allot, then put the pistol down. Where I live, Alaska, allot of new arrivals will buy one thinking they need bear protection when going from home to the gas station or commissary on base - too funny. We see ALLOT of 500 S&W used for sale. This is also a pistol banned/prohibited from use at most club and municipal indoor ranges.
Rifle - 50cal BMG. My local stores sell the ammo. If you had access to 2-3 miles of open country and some shooting skills - I can see this would be allot of fun - and near addictive! However, if you don't have access to wide open country - good chance you will be screwed because many ranges prohibit this rifle. It is louder than most other shooters on the range are protected for.
Clint Eastwood (Dirty Harry) liked the 44 mag. In handguns it is very powerful unless you start into exotic and rare calibers. In rifles, look to Weatherby for some great calibers. North American big game, 338 calibers with muzzle speeds over 3000fps will stop most game. African game need a little more bullet( larger bore and higher grain wt).
That would depend upon much.