I'm leaning towards a Labour degree. Law is awful, placement rates are low, and the work is hell. It does have some of the advantages you mention and in the US is probably better for politics since you don't have a Succdem party. But you'll do a lot of amazing low level work with the labor studies degree, especially when most graduates only do union work as a stepping stone to anti-worker corporate positions.

I'd point out, at least here in Aus, a Labour studies degree isn't a bad thing for advocacy. It'll get you a spot at the Left faction or the Labor Party or the Green's table easily if entryism is your thing. A number of our best Labour Prime Ministers have come from union work.

But ultimately, both are good choices, do what you enjoy the most and what fits your skills best. The revolution isn't supposed to make you unhappily sacrifice.