I think that it is misleading to advertise any tour, equity or not, as "Broadway" because many naive theatre goers assume that they are seeing the same cast that they saw perform on the Tony's. It gives the impression that the Broadway production has picked up and begun traveling.
Last year I toured Equity for the first time, and it wasn't very different from my non-equity experiences. Granted it I was signed on as a ASM (in addition to being a performer), so it wasn't your typical big Equity musical, but the production company followed equity's procedures and policies. I don't feel magically more talented now that I have my Equity card.
If I can't find work at all, I plan on dropping my Equity status, because I would rather tour non-union and get to perform than sit around with an equity status that I have nothing to do with. But I'm giving life as an Equity actor a shot.