Does NXT have any unique plans that cannot be solved easier on the more flexible Ethereum platform?
Indeed.
1) Smart Contracts -- Not Turing-complete but covers basically 99% of all smart contract problems (trust me contract writers do not need Turing-completeness)
2) Automated Transactions -- Turing-completeness addition to Nxt; for the 1% other applications that require more elaborate algorithms
Btw. more flexible is not easier. In fact, most of the time it is the other way round. With more flexibility comes a steeper learning curve and bigger amount of mistakes made.