"NT or EH?" assumes the two cards compete for the same days out. They mostly don't. The National Trust is coastline, landscape, gardens, great houses — and, crucially for a 2.98 m-tall van, an enormous estate of car parks in exactly the honeypot places where parking is the whole battle. English Heritage is the monument record: castles, abbeys, forts and the entire drumbeat of Hadrian's Wall — smaller sites, denser history, and some of its best ground (Berwick's walls, Castlerigg's stones) free to everyone anyway.
So the useful question is never which brand is better. It's which map does this year's touring actually cross? The eight expedition files give a rare evidence base: every planned day, both cards, honestly scored.