What is more expensive and or slow

So i have 2 options to do some backend query filtering. But i was wondering which of the 2 options is more expensive and/or slow.

Option 1: do a backend query filter on a Collection Field that has data type String(from dropdown selected option):

Option 2: do a backend query filter on a Collection Field that has data type Document Reference(from dropdown selected option):

Which of the options is more expensive and/or slow?

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