[smtlaissezfaire]

As far as I understand it, MVP is all about determining whether there might be customers out there for you. (It's answering the question "Is anyone actually going to buy this thing?").

So staying small and out of the public spotlight to iterate on failure is valuable (and doesn't produce any negative PR).

If you have to go open beta to get that feedback, then do so. If you can get away with a private beta, do so.

Here's the better question: Can you set up a system so that you don't even need any sort of beta to tell?