Brand name of course helps, but I think it comes down to the role you are doing and the line you are in. Does either role value add to your skillsets?

When you mention big 4, I assume you are an accounting grad. I would like to think the top accounting grads head to either banks or big MNCs finance MA programs. For the rest of the students, its like a factory, but no harm no foul I suppose. Starting off in big 4 doesn't hurt (save the salary). I would definitely choose big 4 option other than some no name company if that were the case.