Unfortunately I can't say much of Diners Club because here in Mexico the card is no longer available. As a formet Citibank employee, we all had them and never used the lounges, but I can tell you about the American Express lounges. As a Platinum member, I have access to Mexico's Centurion Club and it worth the price. You have a club with a superb atmosphere, complementary drinks, snaks, newspaper, etc. there is a money exchange office where you can buy any currency you need on your international trip, plus you can pay your Amex card. I know that AMEX has lounges in Germany, Ecuador and some other countries. I am just happy to have access to them.
Other benefit for Amex Platinum members is access to Northwests Worldclubs and Continentals Presidents Clubs if you have a ticket to fly on any of this two airlines (doesn't matter if you fly economy with discounted fares or ff benefit).
Hope this post helps you.