think of it like this...
you drop a ball from a fixed position onto the peak of a two sided ramp (^) you drop the same ball from the same spot over and over and count how many times it goes one direction and how many times it goes the other direction. you can then assign a probability of how often it will fall to one side or the other. now, no matter how much data you collect, and no matter how accurately you can predict the outcome based on probability, there is no way to say with certainty which way the ball will roll.
same thing here, only much much bigger. while some things may have the same outcome, that does not mean you will have the same universe. say the re-made universe had the exact same laws of physics and the same gasses present at it's creation, they wouldn't produce the exact same planets as we have today. the interactions would change the outcome. while it may be similar, it will not be identical.
the fact that information cannot be destroyed also does not dictate that the same information will be dispersed in the same way. the new universe will may have the same number of water molecules as our present one does, but there may not be one drop of liquid water in existence. all the ingredients for life may be present, but again, no guarantee that life will start to exist, or if simple life did start, it would not evolve in the same way, so again, you and i would not exist.
given the fact that the universe is continually expanding faster and faster, this is of course a moot point, but a very fun philosophical question none the less.
thanks for posting, this one was fun to ponder :)