Depending on the employer and the side-project, using the same account for both could _in theory_ bolster a (ridiculous, absurd) ownership claim over your work, for example. Stranger things have happened.
More pragmatically, I've been burned in the past by using personal accounts (not GitHub specifically) for work things. For example, I used a personal commuter card for a former job's benefits program. When I left, they deactivated my card. Awkward! Not the same kind of risk with GH, to be sure, but after that I do prefer to keep my digital selves as compartmentalized as possible.
What sorts of separation are beneficial for you? I'm wondering if I should switch, but I don't fully understand.