Vue.js is a progressive front-end framework developed by Evan You in 2014, known for its gentle learning curve and ease of use. It offers a component-based architecture and uses a virtual DOM to improve performance. Vue has a simple template syntax with HTML-based templates and single file components that contain HTML, CSS, and JavaScript all together. The project structure of a Vue app is organized in a specific way, with the public directory for static assets, main.js as the entry point, App.vue as the root component, and various directories for child components, router configuration, state management, and more. On the other hand, React is a JavaScript library developed by Facebook in 2013, also used for building UIs and SPAs, with a component-based architecture and virtual DOM to improve performance. React uses JSX, a syntax extension of JavaScript, to describe UI elements, and has a more opinionated approach with built-in tools for state management and routing. Both frameworks have their strengths and weaknesses, with Vue being easier to learn and integrate, but React having more support and backing from corporate giants and a larger community. Ultimately, the choice between Vue and React depends on the specific needs of the project, including team experience, application complexity, and desired level of customization.