Oops, I confused FANNIE MAE with GINNIE MAE, my bad.
Besides private profits and public losses, there are also differences in regulation and level of long-term risk / guarantees.
Simplistically, what they are actually trying to do is to recreate another, bigger, public-private GSE (MCGE) from remnants of Fannie and Freddie, offload "bad assets" to taxpayers ("bad bank"), get the "good assets" to private investment firms ("good bank"), and guarantee any losses to them.
GSEs and public-private enterprises are actually favorite ways of socialist / fascist strategists under the guise of Third Way economic structure. Tony Blair was the most ardent proponent of Third Way, with Clintons just slightly less explicit - they didn't use the name.