should one use JavaScript or PHP to handle a cookie data?
To make this a little more general, let's call this "Client side" (which is almost exclusively JavaScript) and "Server side" (which can be PHP, JavaScript or any other language) code.
The short answer is that: It depends what you are doing with the cookie data.
Most of the time, dealing with cookies server side is simpler.
Sometimes, the information in the cookie needs to be secure, and you don't need to access it from client side code, so you'll set an http only flag on it so that if you suffer an XSS attack the damage is limited.
Sometimes you will want to avoid making a server round trip (to take a trivial example: You allow the user to pick different stylesheets for your website. You don't want to reload the entire page when their change their preference. You use client side code to change the stylesheet currently loaded, and client side code to store that preference in a cookie. In the future, when other pages are loaded, you can use server side code to set a different <link>
element.)
Do you use javascript to get cookie and than pass it to PHP to do all the filtering ?
You might use client side code to set a cookie value, and then use server side code to read it. There is no point in using JavaScript to read it and then using some non-cookie based mechanism to send it to server side code. That just makes things complicated and more likely to go wrong.
Do you use PHP to do all of the stuff?
Only if all the stuff is better done with PHP
Which one of the above will improve performance or is there another way?
As is normal with questions of client side code vs server side code: If you aren't loading a new page anyway, then using client side code is usually faster.