As @yogthos@lemmy.ml mentioned, they differ in implementation:

• The Hy compiler works by reading the Hy source code into Hy model objects and compiling the Hy model objects into Python abstract syntax tree (ast) objects. In other words, at runtime it is essentially Python source code. Similar to Typescript and CoffeScript (JS).
• Basilisp is hosted on the Python virtual machine, so its compiler generates native Python bytecode. Similar to Clojure and Scala (Java/JVM) or Elixir (Erlang/BEAM).

Personally in these cases, I prefer the second approach, because the first one is basically "syntactic sugar": a Python lispy syntax (embedded), on the other hand Basilisp is a "more complete implementation", that is, a language independent of the host language with all the strengths and weaknesses of its host system/VM.