HBase and Accumulo are both implementations of BigTable using HDFS as their storage mechanism. They are virtually identical in most regards from both an operational and architectual standpoint; they have different APIs, and use different nomenclature, but conceptually they do the same thing and performance is close enough that there's no significant advantage to using one over the other.
HBase has a much larger user base, better support, better integration with the rest of the Hadoop ecosystem, and a better set of peripheral tools.
Accumulo's point of differentiation is security. It offers fine-grained access controls, down to the field level, that HBase lacks, plus many other security-related enhancements. That's really it's only advantage, but if you are dealing with sensitive data, not having that level of security can be a showstopper.
- Joe Pepersack, Big Data / DevOps Architect, Perl Hacker, Pseudopolymath (https://www.quora.com/How-do-we-compare-Apache-HBase-vs-Apache-Accumulo)