I think Ben Lamb has it right...all depends on definition of trophy.
If you're looking at it just from a B&C or P&Y score to define a trophy, then no, its no different. The animal is what it is if all you're looking for is the score. In other words, a 180 inch mule deer buck is the same deer whether its on public or private. To add to that...a 150 inch buck shot on public with a bow doesn't make that any better trophy than the same deer shot on private with a rifle...still the same deer and still the same score.
But if we define trophy from experience, rarity of an animal in the area you hunt, then I say Yes, there absolutely is a self-defined difference.