Well, I don't agree that it's both in the slightest. The FEC attempted to justify prior restraint on speech by making a spurious argument that speech is equivalent to money and is therefore within the scope of its power to regulate campaign contributions. The court ruled that no, speech remains speech regardless of whether money is spent to facilitate it, and is always under first amendment protection.
Further, the problem with unlimited campaign donations -- i.e. actual transfers of funds into the hands of candidates -- is that it creates a situation in which a given candidate might become materially dependent on a specific individual or organization to the point that it creates an entrenched quid-pro-quo relationship that would control the exercise of their duties in office.
But in this case, the complaint of "billionaires spending unlimited money on politics" doesn't describe an instance of that problem at all, because the money is being spent in an attempt to persuade voters, not create patronage relationships with the candidates themselves.
The elections are still up to the voters, and to describe people using their resources to publish their opinions in open discourse as "anti-democratic" is exactly backwards -- creating an apparatus that can preemptively restrict what political information voters are allowed to see is about as anti-democratic as it gets.
> (in a similar, but less extreme, way as total one-party control of the media is)
The closest thing to "one-party control of the media" being threatened here is a situation in which a state body (ultimately under the control of incumbent politicians) is allowed to preemptively curate what information may be distributed by the media. This is the exact thing that the Citizens United ruling put a stop to.
