I bought both cork and synthetic and found that they both have pros and cons. It depends on your habit of muting. I like the slightly more compressed feel, the ease of keeping it on the bell, and the reliability of the synthetic cork. However, it can get stuck if you push it too hard into your instrument, which compromises the moment when you need to change mutes quickly.
I like to insert the mute with a light twist without worrying whether it is too loose or not. With that in mind, I prefer the synthetic cork to the traditional one, which I like and don’t mind using at all.
The fact that it costs only a few dollars more than the cork ones makes me swap it whenever I need to replace my mute cork.
And I hope there will soon be synthetic cork for the practice and the Harmon mute.