About copper & half round gutters
Most gutter in the valley is 5 inch K-style aluminum, and for most houses that is the right answer. Copper and half round are for the jobs where it is not. A restored North End bungalow, a custom build where the architect specified the profile, or an owner who has decided the gutter should look like it belongs on the house.
Half round is the older profile, a true semicircle rather than the ogee shape of K-style. It carries less water per inch of width, so it is sized up rather than swapped like for like, and it is usually hung on external brackets that are part of the look instead of hidden hangers. Getting that spacing right matters more than it does on K-style, because there is nowhere to hide a sag on a curve.
Copper is a different material to work as well as a different price. Corners are soldered rather than sealed, which is why a properly made copper mitre outlasts the roof it is fitted to. It also weathers. It arrives bright, dulls through brown over the first year or two, and eventually takes the green patina people are usually buying it for. Nobody should spend copper money without knowing that timeline.

