As an Australian that moved to the US a few years ago and does a lot of flying for work, I'm on the fence when it comes to airport privatisation proposals. One of the interesting differences between the US and Australia is that, despite the fact that the US is generally more in favour of private sector delivery of services (think healthcare etc.), it has overwhelmingly kept its airports publically owned. Most major airports in the US are publically owned, whereas I think every major Australian airport was privatised many years ago.
On the one hand Australian airports are wayyyy nicer than US airports. More modern and up to date, cleaner, more spacious, better and more facilities etc. Nicer places to be in by a long shot. US airports, especially some of the major ones (Newark and O'Hare spring to mind) are very overcrowded at peak times, straining at the seams and generally just more unpleasant places to be in (e.g. what's with those disgusting old seats and claustrophobically low ceilings in Concourses E/F at ORD?)
But why are they so much nicer? Because they charge a lot more and thus have a lot more money to pump into improvements. US airport parking fees, even in a major city, are a small fraction of what they are in Australia for instance. I could park at Chicago for a week for what it could cost for a few hours at SYD or MEL. Australian airports no doubt also charge the airlines more than their US counterparts too (landing fees etc.), which indirectly affects ticket prices etc.
So in terms of user experience, private airports seem nicer, but in terms of equity of accessibility to travel itself, publicly owned is the way to go. Prices go through the roof when airports are privatised, if Australia is anything to go by. Travel should not be only for the wealthy.