When comparing Scala.js vs Web Components, the Slant community recommends Scala.js for most people. In the question“What are the best solutions to "The JavaScript Problem"?” Scala.js is ranked 17th while Web Components is ranked 29th. The most important reason people chose Scala.js is:
Scala offers type inference, which, while giving the same safety as Java's type system, allows programmers to focus on the code itself, rather than on updating type annotations.
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Pros
Pro Type inference
Scala offers type inference, which, while giving the same safety as Java's type system, allows programmers to focus on the code itself, rather than on updating type annotations.
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 Easy, type-safe, interop with JavaScript
The JavaScript-interop of Scala.js is very direct and lightweight.
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 Extensive standard libraries
Scala.js implements most of the Scala standard library and many parts of the Java one. Among others, it supports Scala's rich collection library.
Pro Dead-code elimination
Scala.js performs dead-code elimination out of the box (when running in the "fullOpts" mode).
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 Crossbuilding
Keeps your client and server sources in sync.
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 Excellent tooling (IDE) support
The same good and mature tooling that can be used for Scala can be used for Scala.js out of the box (code-completion, refactoring, immediate feedback, etc.).
Pro Immutable values
The immutable values make it perfect for working with concurrency.
Pro Macros
Because Scala.js is a plugin to the Scala compiler, the whole power of the Scala language is available at compile-time. Which includes macros. Very expressive things can be done, in a type-safe way, which are difficult or impossible in other languages.
Pro Simple build system compared to Javascript
While SBT is arguably not as simple as Maven, it beats the chaos of the JavaScript build ecosystem.

Pro Great for small—likely published—reusable libraries
Very extendable as a single-import base layer for visual controls and probably also something like a react-redux Provider.

Pro Works with any framework
Less recreation of the wheel and fewer wrappers.

Pro Fallback styling when not yet defined
Before a component's script defines the custom element—either as the page is loading or with JavaScript disabled—it can be temporarily styled via :not(:defined)
. This may prevent the need for SSR.

Pro Customizable templates via custom-recognized "slots"
slot="name"
and <slot name="name">
for customizing a component's HTML in specific areas of its shadow DOM. Also fallbacks when not defined.

Pro Stylable via custom-exposed "parts"
::part(name)
pseudo-element for styling elements within a component's shadow DOM.
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

Con Not well-suited for application wiring
Having to serialize/deserialize data between components is not convenient. You'll probably still need a [light/simple] framework. Some things are still quite nice, such as using the light DOM -- think <option>
with <select>
and <datalist>
.

Con SSR is potentially more difficult
…if you need more than CSS' :not(:defined)
, that is.
Check out this video to see how the creator of SkateJS handled it: https://www.youtube.com/watch?v=yT-EsESAmgA
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