Being an economic liberal, I always thought that this was one of the main advantages of the EU. Setup shop in one country and sell to the whole single market while encouraging beneficial tax competition. I do oppose special deals for specific companies though. Ireland, please stand up to the Brussels cartel!
The problem is that it gives large multinational companies a strong competitive edge over single-national companies, and it makes tax money bleed from high-tax countries to low-tax countries. Both of these things are also self-reinforcing, accelerating the process.
(Not that I have any solutions to these problems, I'm just pointing them out. :) )
"Tax competition" is only beneficial to the rich and to smaller states that can steal taxes from bigger ones. But of course, if you oppose free schools, free healthcare, and you favor the rich getting richer and the poor getting poorer, I understand why you like it.
Corporate tax is one of the most damaging forms of taxation in terms of the number and size of distortions it creates in an economy and it is very damaging to national competitiveness as well. But being in favor of lower corporate tax does not preclude supporting various other wealth redistribution schemes to help the poor or reduce inequality.
If the EU is more concerned about the specific case of internet giants rather than multinational firms in general, they could tax this in a much more practical way by having state run internet service providers charge these content companies for access to their markets.
What is the advantage of tax competition? Small countries that only host headquarters can charge very low rates: they don't have most of the expenses of bigger countries, especially if they are under no military threat by their neighbors and therefore protected by them.