To answer the edited question: in short, it is beneficial to use LINQ whenever you have to implement "query" functionality (that's what the Q in LINQ stands for).

To elaborate slightly, a lot of query functionality has been brought directly into the language (or rather, the various LINQ-implementors), so things like aggregations, ordering, grouping, filtering (and many more) are all handled for you.  The LINQ-based solutions are also typically far shorter than if you were to implement them by hand, and also communicate their intent far better.