Interoperable. Write a component and use it in any framework. Sorta. React is kind of a pain still...
You can write more flexible, more customizable versions of native HTML elements with better defaults.
Writing flexible, composable components is super difficult. One of the primary goals of web components is encapsulation of styles and functionality. Which is nice in some cases, but when you want it to be flexible and usable in a variety of situations, that encapsulation can fight you a lot.
There's no built-in context like in React. If you want a channel for related components to communicate with each other, you have to use something like Redux or roll your own.
Extending native HTML elements is kind of excruciating. Say, you want to create a web component that just extends an HTML
<input>with a little extra functionality or custom styling. You can't really expose the inner
<input>component, so you basically have to re-implement all the attributes and functionality of that input manually. For an example, see how complex it is to implement a basic custom checkbox element.