This seemed like a trivial question to me... until I began to think about it.
The "usual" criteria for greater acidity are larger sizes of the atom attached to the acidic proton within the same group(e.g. hydrogen selenide over hydrogen sulfide over water) and inductive (and/or resonance, the latter of which usually dominates) stabilisation(e.g. phenol over ethanol); hydrogen peroxide has no reason to be more acidic than water by the first criterion and the second criterion would destabilise the anion instead, with the hyperconjugative electron donation from the oxygen-hydrogen bonding orbital far outweighing the negative-hyperconjugative electron withdrawal into the oxygen-hydrogen antibonding orbital.
So why is hydrogen peroxide acidic in aqueous solution, when it has no reason to be more acidic than water and every reason to be less acidic than water?