In Europe, there are no 'Federal' taxes i.e. at the European level. All taxes are to the 'State'. So it doesn't matter if my analogy is a little bit off.
I am not sure I understand why it makes a difference. If the baseline (federal taxes) are the same everywhere, it's just the same as if there were no federal taxes. States compete and offer special tax breaks on a state level; that's the same situation we had here in Europe, except that the federal government, unlike the EU, doesn't seem to care if states offer a company crazy tax breaks, subsidies, or loans, even if said breaks are a special deal for that company alone.
There are no 'Federal Taxes' in Europe. Corporations don't pay a corporate tax at the European level - just to the states. So there is tax competition.
Right...but the existence of a federal tax is irrelevant; there is still tons of tax competition because the states assess their own taxes. The federal tax rate, from the competitive perspective, is irrelevant because everyone pays it. But every state has different taxes and they compete with each other to give the biggest tax breaks.
For for example you might have:
State A:
State income tax: 5%
Property tax: 5%
Sales tax: 5%
State B:
State income tax: 6%
Property tax: 6%
Sales tax: 5%
Yes, everyone in both State A and B pay, let's say, a federal 7% income tax and payroll taxes. But the state taxes make a huge difference. State says to Wal-Corp - build a store here and you'll be exempt from property taxes and sales tax for 5 years, and we'll give you a special state income tax credit that reduces it to 3%. That's the kind of deal making we have going on with states, except the federal government doesn't intervene to stop it like the EU did here.