The Galaxy S10 has a 6.1-inch AMOLED screen. The Note 10 has a 6.3-inch AMOLED.
The difference between 6.1 inches and 6.3 inches might seem notable on paper, but when you hold these phones in person, you'll hardly notice a difference. Samsung is using its same, top-of-the-line quad-HD technology for both of these phones, and they're a real treat to look at.
Also, while I'd call my hands medium-sized, I still prefer phones be a little smaller so they're more comfortable to hold in one hand. I like the 5.8-inch iPhone XS and 6.1-inch iPhone XR, for example, more than the 6.5-inch iPhone XS Max. In this sense, I'd also recommend buying the phone that's more comfortable to hold, and that's why I like the Galaxy S10 here.