I'm eligible for an Irish passport because my Grandpa was born in Ireland.
I've already got dc so it's too late for them, I'd be the only one of us who had an EU passport. Similarly it might be useful for work but chances are my colleagues will only have UK passports.
There would be no point me breezing through passport control in France if I have to stand in a huge queue when we get back to the UK! Can you travel out on one passport and back on another?