I worked at a management side firm. There is no reason not to take employment and labour courses even if it is not an absolute deal breaker. If you want to work in the area it make sense to get the foundational knowledge in school rather than learning on the go.
As to the firms themselves, I can't really compare them, since I only worked in one. I think things like atmosphere are driven less by the fact that the firm is a management side or union side and more by the personalities in the firms themselves. I would say that you need to be committed to the cause of organized labour if you want to work on the union side, and you need to be able to demonstrate that commitment.
The work itself would be largely similar and advocacy based. A caveat, is that as a management side you'll do things like policy reviews and advising on corporate transactions in a way that I imagine you wouldn't do as a union side lawyer.