Hey! I'm the author of Basilisp. Thanks for the mention here!
Basilisp is much less mature than Hy but tries to stay generally compatible with Clojure, which is somewhat different than the goals of the Hy project.
Cool, I'm a Hy guy; glad to meet you. Hy in its early years imitated Clojure syntax much more closely, and Clojure compatibility may've been implicitly a goal even if it never got to the point of cross-testing. These days we prefer to think of Clojure as one of several possible influences.