UPDATED 2019
I can name some simple points in plain language from my limited experience:
Properties. C++ and Java had this notion of a public getter/setter function "property" wrapped around an internal class variable which led to large amounts of boilerplate code. C# formalized this as a real language feature and reduced much of the boilerplate in C# 3.0 with auto-implemented properties. Scala classes define trivial properties simply as regular read only vals or read/write vars. The class may later choose to replace those with get or get/set methods without affecting client code. For this, Scala provides the most elegant solution with the least language features and complexity.
Arrays use regular generics. In Java/C#, int[] is redundant and confusing vs List or List. Worse, in Java, List has lots of runtime overhead, so many developers have to know to use int[]. Scala avoids that problem. Also, in Java/C#, arrays support (covariant) casting, which was a mistake, that they now can't fix because of legacy concerns.
Scala has better support for immutability. val is a basic language feature.
Scala lets if blocks, for-yield loops, and code in braces return a value. This is very elegant in many situations. A very small plus is that this eliminates the need for a separate ternary operator.
Scala has singleton objects rather than C++/Java/C# class static. This is a cleaner solution.
Pattern matching. Object unpacking. Very nice in a large numbers of situations.
Native tuples.
"case classes" which are what most other languages would call record types or named tuples.
Fancier standard library with more elegant collections.
Multi-line strings. String interpolation formatting.
Optional semi-colons.
Cons.
Java has caught up a lot. Java 8 was first released in 2014, but it took several years for older Java versions to be phased out and the new Java 8 features to be fully used across the Java ecosystem. Now, lambdas and closures and basic functional collections, with support for filter/map/fold are quite standard for the Java ecosystem. More recently, Java has added basic var local variable type inference and has multi-line strings and switch expressions in release builds preview mode.
Scala is complicated. I'd highlight features like implicits to be inherently confusing.
Scala has minimal backward compatibility. Scala 2.10 artifacts are incompatible with Scala 2.11.
Building a Java API for other JVM-language developers like Scala or Clojure or Kotlin is normal, well supported and accepted. You generally don't want to build APIs in Scala that cater to non-Scala developers.
