Some of the things off the top of my head in no particular order; protocols, (closer to traits than interfaces), Optional types, (elsewhere no null types), pattern matching (if let, case let), guards, (so you can cover your preconditions nicely), immutable let bindings first, var variables second, (with mutability being tied to the binding outsite of reference types/classes), tuples, lazy evaluation, flexible closure syntax, fairly powerful type inference, enums as tagged unions, (or as standard C enums if you want), extensions - even for core structures if you need it - straighforward way to define custom or overload existing operators, type system powerful enough to be able to implement a fairly convincing Functor, Applicative or Monad without much effort, structs AND classes, most things are value types...
But most importantly to me, Swift is composed in such a way that it just 'clicks' for me, ie many times many times I can guess how something is likely called or how it will behave without looking at the docs and I have a solid chance of being right - that 'intuitiveness' is something that is lacking in many other languages I've used over the years.
In regards to C#, by now it is definitely not just a Java clone anymore, in particular saner type system and much more functional features edge it for me over Java, plus the speed of evolution is much greater in the C# land.
If you want to see how C# and Java differ but are tied to the JVM, try Kotlin: http://kotlinlang.org - it's fairly similar in feel to C# and has 100% Java compatibility.