I wrote a long response to this last time someone asked this question. Search
/prog/scape for it. It discussed the detailed differences between pseudorandomness, quantum randomness (or merely subjective indeterminism, however I'm not entirely sure I had fully understood the generalized version of this philosophy at the time I wrote that post).
A tl;dr would be:
1) Pseudorandomness may be as useful as statistical randomness for all kinds of things. It behaves well enough for an observer to not be able to distinguish it from true randomness as long as he does not have knowledge of the PRNG's internals.
2) Subjective indeterminism is ``true'' randomness. It merely means finding oneself in some specific MWI branch. In a more general sense, it means being a particular observer having some subjective experience. being an observer in the Level 4 multiverse (even restricted to computable structures only) already gives an unique address and thus a very special brand of randomness. Another way I show what this is... is to have you imagine making 10 atom-exact copies of yourself and putting them in rooms which are only distinguishable by an index number (visible to the observer/"copy") - the index number they observe is truly random, but the system is always deterministic (be it the universe, the multiverse, the larger mathematical multiverse and so on). Subjective indeterminism can be taken pretty damn far and leads to some incredibly strange and alien places, some going beyond even MWI (I can post some relevant books regarding exactly what this is, but that kind of randomness is probably more than
>>1 asked for).
1 is useful for various practical applications where you just need randomness for casual stuff, 2 is the thing that defines your very existence in some ways and has certain interesting applications.
The verdict:
No randomness in the system as a whole. Statistical pseudorandomness is easy to make if you need it for practical applications.
True randomness can be thought as indeterminism from the first-person perspective of an observer (if a number could perceive itself, it might ask itself why is it that specific number).