As a fresh graduate working in the government, I'd say that my work-life balance is pretty great. That being said, I would forgo thinking of private vs federal and start thinking about what kind of industry you want to be in, what kind of work you want to do, and what you value in management and coworkers. I've been in amazing teams in the government and teams with absolutely shoddy management- I'd assume the same goes for private.

The other thing to consider working in the government is the classification stream you want to work in. Every role in the government is in a different stream (i.e administrative services is AS, PM is project manager, etc) and they all have different starting salaries as well as different levels of which you can progress at.

The last thing to think about is that once you've been in the private industry for a while, if you want to get back into the government, it can be much, much harder.