They are similar ideas on the surface, key differences are that we use Elasticsearch as the underlying distributed search engine, InstantSearch is based on Algolia.

Reactive Search also supports more components at this point, most prominent one being maps. We released an entire library https://opensource.appbase.io/reactivemaps dedicated to that earlier and all those are available with ReactiveSearch as well.

The part that I really like about ReactiveSearch is its neat composing of components to form complex search UIs, this abstracts out the need for writing Elasticsearch DSL queries to a large extent.