In short, the Häupl-wing is opposed to co-operation with the FPÖ, rules out a coalition with them on the state and federal level and otherwise fights against the FPÖ.
The Niessl-wing is in favour of co-operation with the FPÖ, doesn't rule out a coalition with them on the state and federal level (or even wants one) and otherwise doesn't fight against the FPÖ and even praises some of their policies or actions.
Read more here:
https://uselectionatlas.org/FORUM/index.php?topic=254431.msg5608975#msg5608975