It does depend on where you are going. In the back country I've followed a game trail and been rewarded with my own private little spring.. But where there's a lot of visitors I stay on the trails to avoid erosion.

To add to your list:

Trail - Having to use the established camp sites or face the wrath of the local ranger, scarcity of firewood (assuming you burn) in those sites.

No Trail or off-trail - Camp where you want to. Little likelihood of the ranger coming by, but if you stealth camp, do it well enough - fines suck. Plenty of down wood but avoid the tell-tale smoke.

Trail - Animals know where the people are and tend to avoid those areas. Does not apply to bears, racoons, chipmunks, squirrels, skunks...umm, did I just say animals avoid areas with people?

No Trail - You may be eaten by a bear, a mountain lion, or Big Foot. Most likely you will just be eaten by mosquitoes. You did go off trail to be one with nature, right?

Trail - Stays within the public areas.

No Trail - Might end up on Hiram-the-hiker-hater's back forty or stumble into someone's pot field (I'd take the former any day - those growers shoot and ask questions later).

Trail - If multi-use, mile after mile of horse/mule/cow droppings can really spoil the hike.

No Trail - Pay attention to the droppings! If you see fresh bear scat start jingling your bear bells. If you see fresh bear scat with little jingle bells in it, turn around and run the other way!

Trail - May be mundane, but someone else tried the other routes, got stuck, got thirsty, got hungry, got bit, got poison oak/ivy, and that's why there's a trail now.

No Trail - Maybe you like getting stuck, thirsty, hungry, bitten, itchy in the name of adventure!