This applies to both taxes and tax-funded services. If you want people to live and work in your town/state/country, you provide them with a good deal for their money...it doesn't necessarily have to be a "low tax" solution.

Oh yeah, and people can't take their land with them. :^) 

Otherwise, this form of competition may be a problem because the wealthy have a lot more mobility than the poor--so governments know that they can screw over the poor without any consequences, but if they want the wealthy to stay, they've got to give into their every demand.

I just want to point out that this issue perfeclty illustrates the logic of the land value tax.

 First, this whole idea of "tax competition" rests on the observation that a person only has to pay taxes to a particular government if he lives within that government's territory (or otherwise expects to receive services from that government). So basically, taxes are a form of rent (price paid for the privilege of living in a particular location), yet the income tax and sales tax are calculated in a manner that is completely detached from the benefits received.

Conversely, the land value tax explicitly connects the benefits (use of a parcel of land within a government's jurisdiction) to the fee paid (the rental value of that land). If government action provides added value to that land, then the landowner pays the government in proportion to the value of those services.

If one government used land value taxation, they would be at a competitive advantage relative to other governments; in other countries, citizens would have to pay both taxes and rents -- in the society with LVT, the government would be funded by the rent payments (i.e. taxes would be effectively non-existant).

The governments would still compete, but on the basis of efficiency (providing valuable services in return for the rental revenues) rather than on something as simple as the level of taxes that are disconnected from the services provided.

In the end, much of this might make little difference, as the efficiency or wastefulness of a government is often accounted for in the land rental values of that society :

With respect to the reduction of taxes on labor and capital, and the effect
this has on the rental value of land, economists throughout history have
observed that, when said taxes are lowered, land rent tends to rise
proportionately. Why? For the simple and obvious reason that, the more people
can afford to pay for access to a fixed quantity of land, the more titleholders
tend to charge higher rents. If, for instance, the payroll tax were abolished,
most of the resultant increase in take home pay would be absorbed by higher
rents. Thus, it follows that the more the tax burden on labor and capital is
reduced, the more the revenue capacity of land is raised by a comparable amount.
(Economist Mason
Gaffney explains this more thoroughly in Ch. 7 of The Losses of
Nations.)