Yep. They don't stamp EU passports, but they are swiped and at least for UK citizens the exit is recorded.

With data sharing becoming more common, I expect the OP's question will become more difficult to answer. Any time an authority gets to see a passport the entry/exit could be logged. Technically this information could be made available to the other nation if the documents are linked.

Eg I have a friend who has a Chinese passport and a UK passport. The UK authorities certainly have her Chinese passport details. Originally she had UK residency on her Chinese passport. This was used to support her application for British citizenship.

She is worried that as the UK authorities swipe her UK passport this data might one day become available to the Chinese authorities and they will learn of her dual nationality.