Public places (parks, baseball fields, schools) have more potential for a large amount of good finds, regardless of size. But the down side is that most have been hunted to death. Finding public land that hasn't been hit too hard is the key. And finding old, untouched public land with large areas to check is the Holy Grail of metal detecting.
I've had limited success with private property, but all of them were small properties (less than three acres). You may get a few old coins and relics, but the quantity is rarely there. The amount of finds per acre is much lower than what you would find at a public spot.
For example, my house was built in the early 1930's. Thought I'd find a ton of good coins and when I first detected it. Nope. Just found 1 Barber dime, 1 Merc and a few pre-1920 wheaties. No big silver and just 2 measly silver coins! This place has been in my family since 1965, so I'm positive it hadn't been detected before.
This is just my personal take on it. Your results may vary...