I did AA->BA on Tuesday w/ a 20 in. carry-on & briefcase, no problem.
As the posters mentioned above, BA/BAA can be notoriously strict about the sizing, i.e. your 22 in. carry-on that you had no problems with flying to LHR will be too large when it comes to the carry-on sizers there. Just make sure it's not overstuffed, etc. that would make it stand out to the carry-on police.