Where are you in Zone 10?
That makes a big difference.
I can plant them in full sun in my Zone 8 near Seattle.
They leaves look a little better with some afternoon shade, however.
Mike

In my zone the green varieties do well in full sun while the variegated varieties need some shade. A heavily variegated variety like my Snowboy needs almost all shade with only bright indirect light.

I lived in zone 10 for 30 years and never saw a kousa.
I would drive my neighborhood and see what was doing well or speak with someone in a real nursery and find out what the locals say.

These are by nature understory trees so some shade is appreciated regardless of variety. Kousa dogwoods typically respond to hot, dry weather - like a full sun location offers in summer - by curling their leaves and holding them straight down.

I agree with Mike (and live in his general vicinity) -- these would be happiest with at least some afternoon shade.

I have a kousa dogwood in zone 7a planted in full sun (6+ hours). It has a little bit of leaf scorch going on and looks wilted often -- leaved are slightly curled and point straight down -- it puts out very few blooms. We inherited the tree with our house, so I'm not sure of its age or if there are other problems going on. The inner, shaded leaves of the tree look amazing and healthy, so I'm thinking the sun is causing it just too much stress.

I'm noticing the exact same thing as ayimera in the same zone. I'm frustrated my landscaper put this here to replace a dying Japanese maple as it did not bloom at all and the leaves are actually turning a purple color which is strange.