I would think “it depends”, and it’s difficult to guarantee you’ll always get the same behaviour.
ISO 14443 smart cards, and that includes EMV contactless payment cards as well as MIFARE cards (including Oyster cards) have an “anti collision” system that enables a reader to detect multiple cards (and actually, at least in theory, to identify each of them and talk to each of them independently).
The EMV contactless specifications state that if the reader detects multiple cards, it should not attempt to process the payment.
However, the big issue is that the performance of cards may be very different (especially related to the size and shape of the antenna embedded in the card), so in certain conditions (distance from the reader, obstacles, orientation, order of the cards…), one card may be detected but not the other, especially in edge cases (when the cards are still a few cm away from the reader).
There are so many factors at play that this may not be consistent, so for the same combination of cards, you may have either one card detected, the other card detected, both detected, or none at all.
If two or more cards are detected, no transaction should take place (which means you are now annoying people behind you as you take time to take one of the cards out of your wallet to place it on the reader). If only one card is detected, you may end up in situations where one card is detected when you touch in and another when you touch out. Not sure what happens in this case, but I wouldn't be surprised if you could end up with two "incomplete" trips charged at the maximum fare!
Your best bet, by far, is to make sure you only ever present a single contactless card.