I have been hosting my wordpress sites on shared hosting

I have been hosting my wordpress sites on shared hosting for years, I have been getting ads for WP specific hosting lately and wanted to ask if I can get your honest and objective take on the subject. Will using such service really make a big difference as far as speed and user experience? Here is an example of a service I am considering https://www.dreamhost.com/hosting/wordpress/
It would be great if you have some services that you tested and can recommend.

Thank you.