Engine choices can be based on numerous things: price, fleet compatibility, manufacturer satisfaction, etc.
SIA's 742's and 743's were all PW....so when they added the 744, they stayed with PW. Makes sense. Their A310's also PW. So really this is more of a long standing preference for PW (and now RR) than dislike of GE. Had their A300B4 & D10 fleet been larger, GE could have established more of a GE preference which could have helped favour a GE 777 or 744 order. It didn't happen.
Incidently, JAL has always been very pro-PW. They operate the PW 742, 743, DC-10-40, MD-11. However, when they added the 744 they switched to GE because they were not happy with PW support. So switches can happen. BA started with GE 777's and now only order RR 777's....hence a mixed fleet.
I dumped at the gybe mark in strong winds when I looked up at a Porter Q400 on finals. Can't stop spotting.