This is both a strawman and entirely irrelevant. What's more informative is what both sides do once in power.
The Democrats are quite happy to cut taxes, subsidize all kinds of corporate incentives (see Amazon in NY), and have not actively taken an antitrust stance since the 90s. Meanwhile, the Republicans are quite happy to have a HUGE government, as long as most of those expenditures are in the military and not in social programs. Neither party is particularly anti-corporate. The Democrats are certainly more willing to reign in corporate power, but this is purely in the marginal sense. Consider that copyright extensions over the last 50 years have enjoyed broad, bi-partisan support. As have pro-corporate trade deals like the TPP.
The most stark policy differences between the left and the right in the United States are in the realm of social and cultural issues: abortion, LGBTQ rights, guns. There is no mainstream party that has a substantially adversarial relationship with corporate power.