Both RxJava 1.x and 2.x are designed to be Java 6+ and thus we can't support Java 8 Streams in any of the versions. This was decided to keep support the myriad of Android devices and versions which won't ever get updated to a Java 8 compatible runtime. If you need Java 8 support, consider using Reactor-Core from Pivotal.
The major difference between the two is that 2.x targets the Reactive-Streams SPI directly and for this, it has been completely rewritten from scratch. We are currently in development preview mode which you can access as described in the 2.x branch readme.
The complete rewrite of 2.x improved our memory consumption and performance considerably; here is a benchmark that compares various versions and libraries.
On the API surface, we plan to keep supporting all operators that are present in 1.x and likely extend both versions with new ones for a few years before support on 1.x ends.
Since 2.x is a new architecture, many depending libraries (e.g., Retrofit) has to be updated as well; which likely won't happen earlier than end of this August or may as well take several months to catch up. Here is the wiki page that contains the highlights of the differences.