I think that's the age old debate, just on a smaller scale.
I suspect the answer will still be 'Personal preference'.
I've gone .177 with mine because I quite like to target shoot with it and, this calibre will give me the option to join the competition at the club again.
Also, if I do decide to hunt with it, it'll be used at closer ranges (rats in chicken sheds, birds/squirrels in the woods) but, I'm still happier knowing that I have a faster pellet with a flatter trajectory.
For what you're after, I reckon a .177 with hobbys will put a nice hole in a rat but