Yes, you may get a performance improvement with nvarchar max due to the differences in how the data is stored as described and analysed here
Another plus for moving to NVARCHAR MAX is the greater flexibility over ntext, plus ntext is being deprecated in favour of NVARCHAR MAX
The likely improvement in performance should be minimal when compared to a suitable index
Edit:
When talking difference in execution times, this may be due to cached execution plan reuse/data being cached. If you're going to try optimising this, either by changing indexes or changing data type, make sure you compare performance fairly to make sure you don't get biased results.
You can do this by clearing out the execution plan cache and data cache, though not recommended doing on production server:
DBCC DROPCLEANBUFFERS -- Clear data from cache
DBCC FREEPROCCACHE -- Clear plan cache