I've had all three as Contender pistol barrels.
I agree, the 7-30 Waters is a great cartridge for multiple uses. Developed for lever guns, but like many cartridges designed for other platforms it does even better in TC's with a wider range of bullets than can be used than in a tube feed firearm. Excellent choice for deer hunting. Factory ammo available without reloading.
The 32-20 has its places too, another lever gun cartridge. Long ago it was in use in revolvers for law enforcement. Great for small game, IMSHA, and ammo is available. I shot IMSHA with an old Colt Police Positive Special 32-20 years ago, and from about 3 decades before that for small game hunting. The TC barrel was used for same.
The 445 Super Mag was developed for IMSHA. It could be called a 44MAG on steroids, but you can shoot 44MAG and 44 Special in the same chamber. So it has about the same uses as the 44MAG. Ammo is also available for it.
Of the three in TC pistola's I got the most use out of the 32-20. Had too many others that equaled or exceeded the other two, but the 32-20 was a good companion to the 32-40 Win barrel I also had.
HTH,
Larry