As an engineer or researcher, is it better to work for the federal government or private companies?

I would say that both sectors, private and government, are good for working as an engineer and a researcher. But you say that you are into biomedican engineering/biotech. I would first like to say the 2 main differences between the public (government) sector and private sector. Public sector offers a more secure job with, in many cases, a very good amount of benefits. However, the chance of doing something "cool" just because you are curious is low. On the other hand, private sector enables you to pursue almost any curious questions you have (as long as you can show it's importance). But unless you are in one of the leading biomed companies, benefits aren't as good as the public sector. Also, the job security is not wonderful because they can lay you off almost anytime they want. From salary perspective, you are probably more likely to make more money in the private companies per year compared to as a government employee.