Deregulation of corporate speech does give unions more ability to campaign, but since unions are in frequent conflict with corporations it becomes and issue of relative wealth. Think of who would benefit if the cap on individual political contributions were raised from $2,300 to $230,000. Since most of us can't even hit the cap affordably, the benefit really goes to the wealth few for whom dropping $230,000 isn't a crippling blow. The first problem unions will have from this is caused by the fact that most locals have a treasury much smaller than the wealth of the company with which they negotiate. So it stands to reason that the company gets "more speech" since we're now counting speech in dollars. The only cases I can see where the union can benefit is if the union has a conflict with a relatively small business and the local union has the backing (and we're talking money backing, not the "we stand in solidarity" backing) of other locals or even the state or national levels of the organizations. For example if SEIU is trying to organize the employees at a hospital, they could funnel money/speech to the local there and if the hospital isn't part of a big network it can be outspent. On the other hand, even some of the largest unions now face the prospect of being outspent/spoken by the companies they deal with. For example, the UAW is a very large union with considerable wealth but the Big 3 (need of bailouts aside) probably going to be able to figure out a way to use more money for political purposes. So really, corporations benefit most because they have more money.
A second problem is that unions already have some restrictions placed on them can be seen when one reads Robert Reich's recent article
http://robertreich.org/post/347547700/its-time-for-a-shareholder-protection-act although it might be possible that these laws will now be unconstitutional.