These are very similar taxes: A business takes its revenue and subtracts its expenses, the tax rate is applied to what's left. The distinction is that VAT is paid to the jurisdiction where the corporation's customers are, whereas corporate income tax is paid to the jurisdiction where the corporation files paperwork. It should be obvious what happens when you do the latter: International corporations start filing their paperwork in the countries with lower tax rates.

To fix this you need to tax corporations using a different kind of tax which is tied to some actual activity happening within the jurisdiction, which is what the US has been doing piecemeal rather than all at once, with corporate income tax playing a smaller role as time passes.

Under classical economics, there's also another effect at work. Corporate income taxes are capital taxes, whereas the VAT is a consumption tax.

Under "spherical cow in a vacuum" economics, capital taxes wind up reducing wages in equilibrium. The idea here is that investors care about their after-tax return, and if corporate taxes (on profits) go up they'll simply forego less-profitable investments to keep the marginal return on capital at the right level. With less capital investment, workers are less productive, and under the same spherical-cow assumptions workers are paid in proportion to their marginal productivity.

Conversely, VAT is assessed on consumption but not investment because corporations receive a VAT rebate on their inputs. The same "taxes are a disincentive" effect orients the economy towards investment (on the margin) and away from consumption. Capital intensity, productivity, and wages increase in equilibrium.

Reality's messier, of course, and economic academia engages in lively debate about the real incidence of all of these taxes.