I'd argue we need both massive antitrust, and higher taxes on the wealthy to prevent them from amassing the power to prevent the antitrust.
The things amassing power to prevent antitrust are corporations, not individuals. It does nothing to make Bill Gates sell shares in Microsoft to pay taxes when the corporation stays the same size. If anything it makes it worse because then more corporations are controlled by Wall St rather than founders and they're significantly more inclined to turn the screws to juice short-term profits.
Plus a systematic way of keeping the Gini coefficient of wealth small in a sustainable way. I'm a fan of establishing sovereign wealth funds whose dividends are paid out equally per capita for this purpose.
And change in laws regarding the legalized corruption (Citizens United, ...). And fight for real freedom of speech.
This is very complex problem that needs to be tackled from all sides simultaneously, the entrenched interests are already well setup to defend themselves.