You can use LocalDB in a production environment but all the standard things to consider apply such as limitations on data, performance, etc. Compared to Compact it should be better in all regards as it is effectively SQL Express but it does take advantage of query optimizations that Compact couldn't but you should always test your queries. Note that you still have to install LocalDB so there is also the debate about simply using SQL Express instead but you'll have to make that decision.
You can read more about LocalDB vs Compact here.