If you are in a non-private federal detention center, you are eating better than most of the planet and most of the USA. Private however, you are likely to die earlier for every year spent, exclusively from diet.
This is correct and the list of private federal detention centers is very small and often only used as hubs during transit or court. The most popular one I knew of being Pahrump in Nevada.
Unlike public facilities the food there is much worse, but the guards are paid much lower and have significantly less training. The result is that they more-or-less don't want to get involved in anything and the facility as a whole goes out of their way to keep inmates occupied with things. The result is that they have up-to-date gaming consoles like Playstation 4 with a decent selection of games and because their guard staff is underpaid a much larger amount of drugs make it into the prison on a regular basis. The story from most who rotated through these facilities told me it was more or less just a "party pod".