Expectations for Resolution

Often when rating telescopes the reviewers will report how well certain double stars are split. Since this is not new I was wondering if someone had a handle on exactly what is to be expected from different sized apertures. I have a 120mm refractor that can split the double-double in Lyra very well. This is likely the norm for a refractor of this size but it would be nice to know what to expect from different telescopes as this would make buying decisions easier.

Thanks for the information everyone. Now all I need is a listing of how many arc seconds seperates some popular double stars I know to test my optics. Does anyone know the seperation in the double-double in Lyra for example?