The places you choose to work in, with an environmental major, really depends on the career path you choose to take. Working for a government agency and then transferring to the private sector is beneficial if you are looking to eventually work in consulting or as an environmental professional in a private company to assist in such aspects as regulatory compliance, risk abatement, and environmental testing. You would get a wealth of experience on the regulatory aspect by working for government, and you would get an understanding of the requirements that companies need to meet.
However, you really have to ask yourself why you chose an environmental major in the first place. You may be happier working in conservation for a nonprofit, or maybe you will just choose to work for government to enforce and implement the rules that protect the environment and public health. Environmental professional work in such a variety of fields and sectors, that it's worth doing your research to see what appeals most to you.
Personally, I started in private industry and moved to the federal government, which is where I work now, and I couldn't be happier. I'm sure as you give it more thought, you'll make the right decision and choose what's best for you. Best of luck!