The BA 767s were well and truly shagged when I used to play with them.
The RB 211 is a much heavier engine than the others (and far less reliable). BA had to ground the entire fleet shortly after delivery as the pylons were cracking. Then in the following years they started having big problems with the Brakes disentegrating.
We used to look after a few third world 767s with all other engine types with no problems whatsoever, whereas the 'Black hand gang' were boroscoping the BA ones practically every turnaround.
Go 767 by all means but don't touch the BA ones!