Environmental Engineering and Engineering Sciences both sound like excellent programs. In order to choose between the two, I suggest researching what types of jobs graduates with these two majors hold and see what interests you. Whatever your engineering discipline, you can apply your degree in several different fields. For example, I am an environmental engineer and I work as a Project Manager for a consulting firm. I assist all different kinds of industries with obtaining environmental permits and applying the environmental regulations that may affect their industry. Other environmental engineers I know are environmental lawyers, business owners, or work for large chemical manufacturing plants.
In response to your second question, there are a variety of possible degrees that could lead you to Green Building design. Certainly architects and environmental engineers could work in that industry, but there are several other disciplines that could be involved as well. For example, civil engineers could research more environmentally-friendly building materials and chemical engineers could research a new chemical that could be applied to that building material to make it even more energy efficient. A degree in engineering can be applied in a variety of ways, depending upon your interest! Good luck!