Over the years I have mitered thousands of small moldings around boxes, newel posts and cabinet doors. Having used every power saw available for this task, for these small moldings nothing is as fast and easy as an old fashioned miter saw.
Two things create a seamless miter joint; an accurate 90 degree angle and accurate length. A good quality miter box has 45 degree presets that give excellent results, and they tend to stay accurate over time since it requires little force to swing from left to right. And since this saw is hand powered, you can safely hold parts right up close to the blade without risking dire injury. This makes it very easy to exactly position your stock for accurate cutting. The fine toothed blades on miter saws also virtually eliminate splintering at the cut even with complex detail. This provides a better quality joint, less waste, and a lot less filling or sanding.
Another trick to sharp clean miters is to match your cuts. If one half of the miter is cut with the saw swung to the left, be sure to cut the mating miter with the saw swung to the right. That way, if the preset stops are a little off, they will cancel each other out. One might be 45.2 degrees and the other 44.8. As long as they equal 90, a good joint will result. But if you cut both parts on the same side (say the 44.8) then the resulting angle will be 89.6 and a gap may show.
Lastly, when wrapping a post or box with a molding, I do not try and measure. I prefer to cut the first 45 degree angle, then line up the molding and use a marking knife or fine pencil to mark the length. This saves time and re-cutting from the variations that measuring and marking can cause. With this method and a fine toothed blade, excellent results are easy to achieve.
I am certainly not a hand tools only sort of woodworker. My shop is well outfitted with power tools. I try to find the best tool for the job. For working with fine moldings, nothing beats a quality hand miter box.