Is mass+energy conserved when a new universe forms inside a black hole? My understanding is that there are credible theories out there in which the formation of a singularity in a black hole also represents the beginning of a new universe via a big bang. We can't see the new universe because we can't see anything from within a black hole. Further, the apparent size of the black hole to us does not have to equal the size of the new universe from the perspective of someone inside that universe. My question is, is mass+energy conserved? That is, is the total amount of material within the new universe limited to how much stuff has fallen into the black hole, or how much stuff has reached the singularity? If so then it would seem these black hole universes are only a tiny fraction the size of our own universe.
Under the assumption that there is some sort of "Big Bang" scenario, then we are assuming an expanding universe.  General relativity does not require the conservation of mass-energy on a universal scale in a changing spacetime (arguably, GR doesn't even have a concept of energy on a universal scale), so there is no a priori reason why this black-hole-universe cannot be comparable to our own (in whatever senses we pick).  

A simple way to see why energy conservation must be violated, even in a vaccuum, is to first observe that the vacuum energy density is fixed.  So if spacetime is expanding (or contracting), then we are changing the total volume without changing this vacuum energy density.  Keeping the density the same but increasing the volume means more total energy; decreasing the volume with the same density means less total energy. 

We can also easily observe this violation.  You may be familiar with the concept of redshift: light coming to you from a source that is moving away from you (or emitted from a gravitating source) is shifted towards the red side of the spectrum.  This stretches out the wavelength, so the light has less energy.  The energy doesn't go anywhere, it's just gone.${}^*$

We might also note that, with Noether's theorem in hand, we know that time translation invariance implies conservation of energy.  But a non-static spacetime is inherently not time translation invariant, so conservation of energy is not required.

${}^*$ Well, some may try to regain conservation of energy by asserting that there is an energy of the gravitational field to consider.  This isn't adopted by everyone, but it can be done if you're careful with your definitions.  It just doesn't work as generally and easily as you might naively hope for.