Compton Trailhead is the most common route and the one almost every trip report describes. The standard 5.5-mile loop drops about 1,400 feet from the rim down to the amphitheater floor along the Sneeds Creek drainage and climbs the same elevation back out. The descent is moderate; the return climb is the crux of the trip and the reason AllTrails rates the route "hard." The loop is signed and well-defined. Standard time is 3 to 4 hours.
Centerpoint Trailhead is shorter on the map (about 4 miles round trip) but does not descend into the hollow. It ends at a top-of-bluff overlook that gives you the amphitheater from above. The mileage is easier on legs, but the experience is fundamentally different: you do not stand at the base of a 209-foot waterfall, you look down at it. Use Centerpoint if river levels are too low for a worthwhile bottom approach, or if the Compton lot is full.
Indian Creek / Kyles Landing is the river-side approach, 10 to 11 miles round trip. The total elevation change is roughly the same as Compton, but it is distributed over more miles, so the grades are gentler. This is the route to choose in hot weather: more shade along the river bottom, fewer steep sections, and a Buffalo River swim at the end. The downside is mileage and the need to ford Indian Creek, which can be impassable in high water.
One alternative worth mentioning: in March through May the Buffalo River is floatable, and a half-mile walk in from the river up Sneeds Creek is by far the easiest approach if you can paddle in from Ponca or Steel Creek. Local outfitters in Ponca rent kayaks and canoes and can drop you at the right river access.