Flying Concorde was one of those once-in-a-lifetime thrills (actually, I took it round-trip). The windows get warm to the touch from friction and you reach high enough (55,000 feet) to see the curvature of the Earth. Unfortunately, I expect before too long that another Concorde will blow up and the fleet will be grounded for good, just as will happen with the US Space Shuttles. You can never plan for every contingency, and there is not enough quantity in either fleet to shake out serious bugs. Almost no other aspect of modern life could survive a zero tolerance threshold for failure.
In any event, I do not see myself flying on the new Japanese supersonic jet anytime soon.