Would a .22 calibre air rifle make you a better hunter ?
It's like this - the maximum power output of any non FAC air rifle in the UK is 12 ft lbs, no more and probably less (to be on the safe side of the law).
It matters not whether you fire a .22 or .177 rifle, the pellet still only carries 12 ft lbs (max) of kinetic energy when it leaves the barrel.
At 40 yds a .177 will have lost 47% of its energy, the .22 will have lost 43% of its energy (source: Pellant Airgun V.7) not enough difference to argue about. So as far as 'power' goes .22 and .177 are about equal at hunting ranges.
It's an open ended question as to whether one calibre is 'better' than the other, the question will never be answered because of all the different permutations regarding quarry - fur or feather / old animal / young animal /angle of impact / point of impact / winter / summer / range / aerodynamic pellet shape / pellet density and on it goes.
Both the .177 and .22 can over penetrate at close ranges and the .22 may bounce off at longer ranges (I'm sure the quarry would describe it differently !) Either situation is not desirable.
[See page on Over-penetration ]
What does make a difference is whether the shooter can accurately judge the holdover for a given range and hit the 'kill' zone each time.
There will always be stories of superlative shots, but when it comes down to it - can you do it each time ? I'd say "no", because the quarry will present itself differently each time.
What is sure, is that .177 pellets fly flatter and faster making holdover easier to judge than .22 and the .177 may be penetrating at ranges where the .22 may not, always assuming that the quarry presents itself as the perfect target. Of course the damage done by the full impact of either calibre will be fatal.
Inside sensible air rifle ranges both calibres will be effective, but there is an old airgunners maxim which says .22 for Fur and .177 for Feather.
I have used both calibres over the years and I have stayed with .177 rifles, mostly because they were more accurate, but the latest pneumatic rifles are equally accurate - which just leaves the question of holdover !
Now - if I owned a .22 air rifle producing 20 ft lbs of power - that would solve the question for me, but as the legal limit of 12 ft lbs still remains very low (a .22 rimfire produces 110 ft lbs) we have to take all of our shots at sensible ranges and make them accurate !!