If the tax raises all of their costs and it's a competitive market then they'll all have to raise prices, because competitive market = competitive pricing and it has to come from somewhere.
The most common case where it doesn't raise prices is when they don't have any competition and are already charging the monopoly price, so the money has to come from the company because if there was any more to extract from the customer, the monopolist would have done it to begin with. But we don't really like those markets or want to promote their continued existence.
What this doesn't depend on much is the form of the tax. If it's a competitive market then VAT and corporate income tax are both getting passed on to the customer. If it's a monopolist then either one will typically come out of the monopoly rent, because charging the customers more would bankrupt them or cause them to extend the life of used goods instead of buying new ones etc.
However, corporate income tax is generally easier for multinational corporations to avoid than VAT, so they have a pecuniary interest in making people think that VAT is worse than income tax.