"Berkshire has a stake in the US listed Dominoes worth $1.2bn which is trading at 25x earnings and the UK Master Franchisee is trading at 10PE questions on the link."

Not really sure but I suspect it is partially down to the usual premium companies have from US listings and more significantly from the current economy/ growth prospects in the UK, that you touched on, being worse for the UK company.

The UK company I think usually trades around 20x but in recent years has had a fall out with some of its big franchisees but that appears to have been resolved.

Consumer spending in the UK is being squeezed, so rising labour and ingredient costs aren't easy to pass on right now and margins are shrinking. As a result, franchisees are looking to open fewer branches this coming year (I think now 20 down from the 45-50 usually targeted.

I believe it's been growing its market share at the expense of Pizza Hut and Papajohns, and the likes of KFC and McDonalds are also seeing their profits drop, so it's unlikely to be an issue restricted to Domino's. And, going forwards, Dominos are looking at how it can increase automation to help reduce costs. It's also rolling out a loyalty scheme which has apparently gone down well in testing.