To get an intuition for the expressive power you can look up examples of quicksort and factorial in languages that support pattern matching. Haskell is a good example.

It is true that you can always just use if statements, it's more about the convenience and cleaner syntax. You can also do destructuring with pattern matching. Pattern matching is almost a requirement if you are going to use algebraic data types.

As Paul Graham says in Beating the Averages, you have to look at the other language from the perspective of knowing it. Nobody can really explain it. It's just going to seem equivalent or weird syntax otherwise.