You tagged this British English. Food stuffs in the UK are labelled with a Use by date or a Best before date although there are suggestions that this might be changed. So neither of your choices is idiomatic. The difference is that Use before means it might be dangerous after that date, best before just means its qualities might have deteriorated. In fact curiously we do not not use them that much in speech. You would often hear
"Did you receive the parcel? I am a little worried because it contains some traditional pastry that might have gone past its sell by date."
Of course Use by or Best before date would sound just as good.
Of your two options expiry date is used in other contexts like the date by which a credit card or some form of pass becomes invalid. Expiration date is perfectly understandable but would sound unusual.