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Pros
Pro Implements a mature language
In contrast to other options, Scala.js is a compiler plugin for an already existing and mature language: Scala.
As such, it benefits automatically from the existing compiler, from the language design choices made for Scala, which exists and is established in the industry since years.
Pro The strength of Scala on the server
The strength of Scala (JVM) on the server can not be underestimated, and is probably superior to any other choice listed here (where applicable; many have no server-side equivalent).
Being able to use such a powerful language (and ecosystem) on the server AND on the client, and sharing code between the two, is a big advantage.
Pro Multiparadigm
Scala supports both Functional and Object Oriented styles of programming. Beginners can learn both paradigms without having to learn a new language, and experts can switch between the two according to what best suits their needs at the time.
Pro Incremental compilation
Through SBT, Scala.js supports incremental compilation out of the box. That is: SBT automatically picks-up the changes (think "watch" in other tools) and only recompiles what is needed.
This makes the development cycle fast and very pleasant to work with.
Pro Immutable values
The immutable values make it perfect for working with concurrency.
Cons
Con Can be intimidating for beginners
Scala is an industrial language. It brings functional programming to the JVM. All books/tutorials cover friendly aspects of Scala, but there are corners of the language that one can wander into that are not friendly to beginners.
Con A complex language with a lot of incidental complexity that results in significant mental overhead
Con Combines OOP and functional programming for a hodge-podge paradigm
Its excellent mix of functional and OOP programming just like Python to use the tool best suited