The difference is that Pi is apparently normal, up to all extensive existing evidence. The Universe is not normal. Anyway, Physics doesn't preclude Helms Deep.
I think normalness is a stronger property than "possesses all sequences of the alphabet of its digits", since it means that + "all subsequences are equally likely"
Whether that is true is related to the normalness [1] of the number pi, but this property has not been proven. See also: [2].
[1] https://en.wikipedia.org/wiki/Normal_number
[2] http://www.askamathematician.com/2009/11/since-pi-is-infinit...