Hypergrid Business has an article up on Linden Lab restricting use of the Linden dollar in other virtual worlds, OpenSim. See: Linden Labs halts use of Linden Dollars in other virtual worlds.
I doubt this is a competitive thing. L$ incurs a legal liability for the Lab. They have to be able to show the government where those dollars are going. This is a measure of the government trying to control currency and thereby control crime.
If your into philosophy and have read the Federalist Papers, then the fallacy of trying to control crime this way is probably apparent. But, it gives the government more control and feeds the bureaucratic and politicians addiction to power.
Whatever the reason, the reality is L$ are now going to be restricted to Second Life. Expect to see their current use in various places disappearing.