Back in the old days a miter saw held a blade that was attached to a box. The blade was perfectly angled to create 90 and 45 degree angles with a simple adjustment. This manual tool easily cut through frame, crown, or chair mouldings. It even made the cut when it came to exterior corners on baseboard mouldings. Perhaps that is why there are some people who still own and use this type of manual saw and find it perfectly acceptable.
Its All About the Power
Today, it seems that power is where its at, even when it comes to basic tools. The greatest advantage to using a power saw is the cleanliness of the cut. A hand saw, no matter how skilled the craftsman is, still leaves the cut wood a bit more ragged than a power saw. And with the rising popularity of all power tools, there is not a significant cost difference between a manual miter saw and a basic power miter saw.
When it comes to fancier versions of the miter saw, then you must have power. In general, a miter saw or radial saw with allow users to adjust the degree of the cut relative to the fence which guides the wood by a single degree. There are standard stops at the most common settings of 15, 30, 45,...