Folk use .177 more these days as it takes much less skill to shoot accurately at distance.
I've always been a .22 guy, though i have a had a few.177's.
.22 will always take down quarry better than .177.
I can hit pretty much anything upto 80 yard with a .22 running at 11ft/lbs. Anythings possible, just depends how much you want to put into it, and how accurate you are at range estimation
Now come come Bill - I'm sure you and I had this argument when I joined the forum some years back.
While I agree with almost all of your post I feel I must make a few comments.
A .22 is indeed a slower more looping calibre and does indeed take much more skill to hit targets are serious range. However to state that a .22 will always take down quarry better than a .177 to me leaves out a slight detail.
a .22 will do everything a .177 will do - however it has one benefit - the heavier larger pellet will kill cleanly at closer distances - where the .177 "can" over penetrate and simply not kill your target due to less energy transfer (I believe)
IIRC (it may have been another member here Bill?) you hunt at shorter distances than I do. Averaging 25m - at these closer ranges a .22 does indeed have an advantage over .177 - particularly at under 20m. (slower velocity and larger size means more put down at shorter distance compared to over penetration with .177)
However this over penetration is often slated by .22 shooters who seem to forget that this is only at short distances.
This is a generalization but I have known .22 shooters to always go for the "easier" body shot rather than make head shots. (this is also often the case with .22lr shooters who rely on the power of their calibre to do the job)
It takes a skilled shooter to do this and hats off if you can. Personally I dislike this aim point when hunting as in my opinion it leaves too much space for error.
I favour head shots.
What I mean to say here is that slating the .177 because of over penetration is probably only considering body shots. And ignores the whole truth. (it is true a .177 will go through a rabbit at short distance) - Head shots will still kill.
At distances over 35m the .22 will drop more so than a .177 so a .22 shooter does need to know his/her ranges much better to take advantage of the weapon. (a hard skill I will admit.)
The .177 however does of course have that flatter trajectory so it is "easier" to shoot. That is to say that slight miscalculations in range to don't have such an effect.
But the .177 has no less put down capability than the .22 - its just that it is at slightly longer distances.
So there really is no better calibre in my eyes. I would say that the .22 is more versatile but the looping trajectory makes it more difficult to shoot. .177 is much easier to shoot, will easily kill at normal hunting ranges.
If the OP thinks he will require the weapon to be making kills at below 20m on rats and rabbits then a .22 would be the better option.
If however the primary quarry will be rabbits and pigeons at greater distances such as 35m+ then a .177 would be my recommendation.
I suppose it boils down to personal preference and choosing the right calibre for the job.
Frankly if you plan on doing rat shooting I'd get a proper dedicated rifle for it in .25 and do it properly.
Andy