Should I use the native HTML5 date picker when available?

My application is using the Material UI style, and I need to provide a date picker to the users.

I have two options:

  1. Use the native date picker when the browser supports it (e.g. on Edge, Chrome), and a JavaScript implementation as fallback for the other browsers.
  2. Always use the same JavaScript implementation for every browser.

What bothers me about solution 1 is that I don't have control on the level of usability of the date pickers of each different browser. In addition, there won't be consistency between the different browsers.

On the other hand, especially on mobile platforms the use of a native date picker might be preferable for performance reasons, power, and integration with the operating system interface. Take as an example the date picker on Google Chrome for Android.

Which of the two options is best from a UX perspective?