Meeting the standard of true differential privacy is one of the strongest known unconditional privacy guarantees. It will prevent Mozilla from being able to answer any user specific questions. For example, they might have an accurate count of how many people visit Google.com (say 60% of their user base), but they will be mathematically unable to point to exactly which 60% visited the site.
Differential privacy in the RAPPOR implementation is peer reviewed and well understood. We can also review the actual code that ships in Firefox, which is a big plus over the Chrome implementation. There are some caveats -- what epsilon are they setting, are they adding an appropriate amount of noise, how do they protect against repeated queries, etc. but all of these can and will be reviewed by the differential privacy community.
I am not affiliated with Mozilla or Google, though I do work in the field of differential privacy. On mobile now, but I am happy to provide links or answer questions to people who might have any when I am back at a laptop.