In a Big Crunch, would there be more mass than at the Big Bang? I found multiple questions where it is stated that dark energy increases as the universe expands. Assuming a big crunch scenario, will this dark energy "go away" again as the size of the universe decreases again, or will there be more energy (=mass) at the Big Crunch than at the Big Bang?
 A: Point A) The same mechanism that causes the amount of dark energy to increase as the universe expands will cause the amount of dark energy to decrease if the universe contracts.
Point B) A universe that includes an increasing amount of dark energy due to the same mechanism that exists in our universe (in theory) makes it nearly impossible for the universe to begin to contract (not completely impossible in general, but it is for the universe we think we live in). Thus, there will $\textit{probably}~^1$ never be a Big Crunch (unless we're talking about the chocolate bar. I'm led to believe that already exists).
$^1$(probably allows for the possibility that the universe we think we live in is not the universe we actually live in)
A: General relativity does not have a conserved, scalar measure of mass-energy that can be defined in all spacetimes. (Such measures do exist for asymptotically flat spacetimes, but cosmological spacetimes aren't asymptotically flat.) Therefore there is no useful way of defining the total mass-energy of the universe, or even the total mass-energy of the observable universe (even for a closed universe, which is spatially finite). Misner, Thorne, and Wheeler has a nice discussion of this sort of thing on p. 457.
So the question as posed does not have an answer. You could ask instead whether, in a recollapsing cosmology, the local density of mass-energy at time $\Delta t$ after the Big Bang is the same as the local density at $-\Delta t$ before the Big Crunch. If recollapsing cosmologies are symmetric under time reversal, then the answer would automatically be yes. I think the answer to the rewritten question is that you can construct cosmologies that are time-reversal symmetric, but they would be descriptions of a universe that had a maximum-entropy Big Bang, so that the universe was at all times in thermal equilibrium, and there was never any 2nd law of thermodynamics. This would be a universe without observers, which would be a little boring.
Therefore if the question is modified in this way to make it answerable within GR, then the answer is probably that there would be a different mass density at the end that at the beginning (at corresponding times). However, this would have no close logical connection with dark energy. (And it is not true as claimed in Jim's answer that you can't have a big crunch in a universe with dark energy.)
