Generally BA upgrade only for operational reasons, e.g. overbooking with seats available in a higher cabin, or very occasionally for service recovery.

Experience seems to be that BA will upgrade their own elites before anyone in the same tier, and occasionally will upgrade blue and bronze members before gold and silver - other factors may apply here such as frequency of travel/booking and the passenger's CIV score, or it may be a case of late-processed upgrades not going to the correct person.

An a non-BA elite travelling on BA you'd be less likely to receive an op-up than a BA elite, and possibly might sometimes be trumped by a BA blue, but you would be more likely to receive an op-up than a non-member.