If you are buying these two teapots for your mother for making tea, the quality of the clay is most important, and then the size, the density, the workmanship, and the shape. Mark/seal on the bottom is not very important. The first teapot shows that it is made by Li Bi Fang who is one of the most famous yixing artist in China. But the teapot is not made of yixing clay and the colour is not natural. So this is only a decorative teapot, not for using. The second is yixing clay teapot, this is a good teapot for making tea.
To understanding more about how to choose a teapot, manufacture and clay of Chinese teapots, and how to season a yixing teapot, please read our articles about tea ware.