I personally prefer to hunt with a magnum powered gas ram/springer, but it all boils down to the principle of using the right tool for the job.
If the prey you are after is large (and by "large" I mean medium/ large game such as hogs and deer) then a .177/.22/.25 projectile simply does not impart enough force to ethically harvest the animal. In this case, large-bore PCP's have the decided advantage. I cannot help but wonder, however, if modern technology may make large-bore manual-power -meaning spring/gas guns- in large calibers a viable option for hunters, if they could produce enough velocity at the muzzle. Hatsan just released a .30 spring breakbarrel, and although the videos of it do not impress me, it may be a harbinger of better things to come. Perhaps more velocity can be attained in higher calibers by increasing the size of the compression cylinder, although to make a gas-ram with the power of, say, a Dragon Claw would require a cylinder so large it would alter the appearance and usage tactics of the gun. Not to mention the cocking force. But, I'd buy one. Wouldn't even bother to mount a scope with the insane recoil, but it might make a suitable elephant gun- style rifle.
Personally, I enjoy the challenge hunting with a manual-power rifle presents. True, the ballistic mechanics of the powerplant limit your range somewhat, and follow-up shots may take a minute, but that emphasizes even more the skill that is needed to stalk an animal and place a critical shot. Classic "One Shot, One Kill" operation.
Honestly, the skill of the user and their preferred style of shooting is what drives the choice of what kind of rifle they use. I regularly hunt rabbits with my Hatsan 155 Vortex (a .177 underlever gas-ram that pushes most lead pellets supersonic), and in my youth used to hunt them with a single-pump Crosman BB gun. The 155 has even taken care of a population of troublesome feral cats without any trouble. Now, for the ravenous local deer population, even the mighty 155 can do little but "sting" them in the aft quarters. I prefer to use my bow for them (my home town has a marvelous in-city bow season). In essence, use the right tool for you and you will never go wrong.