Doing this guarantees differential privacy, a strong privacy protection.
However, the major disadvantage of RAPPOR is that we get a collection of very noisy data points. Therefore, we need a very big collection to learn anything useful at all!
If the number of clients/users/records is small, RAPPOR is practically useless.
Prio, on the other hand, adds NO noise to client's reports. It uses crypto magic to compute some functions (mean/sum/...) on the collection of reports by a network of servers. Only outputs of these functions are known. No reports are leaked until at least one server is honest!
However, Prio has no guarantee that the computed output doesn't leak information about client's reports (in fact, it surely leaks some information). While, RAPPOR guarantees this protection statistically!
A current research direction is to add noise to the output of Prio as such it guarantees differential privacy.