Transitioning from jQuery to React can indeed bring performance improvements, especially for larger applications.

When we were using jQuery, we faced performance issues primarily due to the direct manipulation of the DOM. Every time there was a change, we had to manually update the DOM, which is expensive in terms of performance. Also, jQuery can become more difficult to manage and reason about as the application grows, leading to bugs and inefficiencies.

When we transitioned to React, we were able to solve these performance issues in several ways:

1. Virtual DOM: React minimizes the cost of updating the DOM by using a Virtual DOM. When the state of an object changes, React first updates the Virtual DOM, which is much faster than direct DOM manipulation. Then it compares the new Virtual DOM with the old one and updates only the real DOM objects that have changed. This diffing algorithm significantly improves performance.

2. Component-Based Architecture: React's component-based architecture helped us organize our application better. We broke down our application into smaller, reusable components, each managing their own state and rendering. This made our application more efficient and easier to manage.

3. Optimized Re-renders and Updates: In React, we can use lifecycle methods and hooks like shouldComponentUpdate, React.memo, and useMemo to control when components re-render, preventing unnecessary renders and improving performance.

4. Code Splitting and Lazy Loading: React allows us to split our code into smaller chunks and load them lazily. This means users only download the code necessary for the page they're visiting, reducing the load time and improving performance.

5. Concurrent Mode: In React, we can use Concurrent Mode to allow the browser to interrupt a long-running render to handle a high-priority event, like a click or a keypress. This can make the app feel much more responsive.

By transitioning to React, we were able to build a more efficient, performant, and maintainable application.