Interesting question - I haven't seen anything written about it. I am a little surprised that NATCA (PATCO's successor, of sorts) favors privatization. Ostensibly, that's because they believe it would lead to more stable and predictable funding, which is almost certainly true compared to the recent history of last minute, short term reauthorizations or interim fundings by continuing resolution.
Shuster's similar bill passed out of committee last year, too, with NATCA support, but never advanced in the House. This year it has the President's endorsement. It will be interesting to see what happens.