1. an language very similar to Haskell
2. a set of runtime libraries
3. a technique for modeling a GUI as a declarative state machine
PureScript only competes with #1 and #2 here. Where Elm really shines is #3, which #2 helps with a lot.
Technically #3 could be done in any language. But it really helps to model it in such an expressive language with immutable data and no side-effects (except via Signals).
https://github.com/paf31/purescript-thermite
https://github.com/kRITZCREEK/reactive-psc
https://github.com/bodil/purescript-signal
https://github.com/michaelficarra/purescript-demo-mario
https://github.com/mechairoi/purescript-frp-rabbit
To me, this is the benefit of PureScript - yes, you have to do a little more work, because you don't get these things for free from the compiler and tools, but you gain complete control over your application structure. You're not forced to work in some ambient Signal category.