I think there should be one rule for all - ie, everyone needs a passport to travel, or, photo ID is acceptable for all. Seems to me that again the british citizen gets the short end of the stick regarding EU rules, they should be the same - EVERYWHERE - for ALL EU citizens.
I don't think the entry requirements are set by the EU, but by each member state. The Schengen agreement sets out requirments for the countries that signed it. The UK didn't.