It's a subtle but huge difference. In React, using JSX means you can create components and mount them
on top of the existing elements on the page.
With Vue's HTML templates, the page itself can be the component and everything can become interactive. For example, you can easily output a HTML table from server-side code, then Vue can convert that into a interactive component while using the existing structure and data.
This lets you render the page using existing web frameworks, it's faster because the server puts it together, it's progressive enhancement and works without JS and on slow devices, and Vue can seamlessly add on top with nothing more than a single JS tag and no compilation step.