They both deal with the environment, but on different but complimentary levels.
Environmental Engineering is based on the design and manipulation of environmental processes to obtain a desired outcome. Environmental engineers apply their knowledge of the natural sciences - chemistry, biology, and microbiology - with their expertise in engineering to solve, prevent or correct environmental problems. Environmental engineers:
- perform an environmental impact assessment
- design or manage systems for water distribution and collection, water treatment plants, solid waste handling and processing facilities, landfills, and air treatment plants
- work with regulatory agencies to review proposals for enviromental equipment
Environmental science is more related to the "environment". They specialize in areas of the environment, such as forestry, soil, water, air and learn the processes that go on within them. Environmental science focuses on:
- healthy human environments
- the sustainability of land, forests and water; the biological, economic, social and technological underpinnings of the bio-products industry
- global food systems
- the challenges of achieving economic, social and environmental sustainability
Between the two, I'd say environmental scientists know more about the environment academically, but the environmental engineers are the ones crafting their understanding and knowledge into usable designs and processes.