It turns out that they are wildly incompatible by default, so directly passing through the regular expressions to RegExp is incorrect in most cases. That was what we used to do before, though. Other compilers like GWT use the same technique.
So I implemented a complete compiler from Java regular expressions to JavaScript regexes that preserves semantics. It supports virtually everything, and fails fast for the few things that are not supported (like grapheme clusters or canonical equivalence). Some things are very tricky to get right, like atomic groups or handling of surrogate pairs when the 'u' flag is not natively supported.
The advantages of that strategy over reimplementing a complete engine (which is what TeaVM does) are a) code size and b) we get the performance of native RegExp's (which are JIT-compiled to native code, these days).