I love Pantheon! The team at Pantheon is amazing, and they are constantly innovating to try and make life easier for developer and their clients. Their hosting platform supports both WordPress and Drupal. I've split my review into two sections, one for business owners and one for developers.
Business Owners: Are you sick of having to maintain your servers? Tired of paying a sysadmin to do work that really can be automated these days? Pantheon has your back, and it makes life SO much easier! Plus, with their support for adding team members, you can add your subcontracted developer during your project and, if needed, revoke access at any time. YOU remain in control of your hosting account without having to give a contractor the keys to the kingdom. It's pretty awesome. And their platform scales effortlessly with traffic. Since it's container based, it takes seconds instead of minutes to scale.
Developers: If terms like continuous integration and automated deployment matter to you as a developer, then you need to check Pantheon out now. There are development, testing and live environments built-in as part of the platform. Multidev is a ridiculously convenient feature, too. Want a branch of your code to experiment in? Sure! Instantly create a fork of your entire site with all the performance of your live environment and start deploying and experimenting. STFP. Git. Support for team members with their own credentials. Varnish. Redis. SAML/SSO support. Site monitoring. Intrusion detection. Responsive support from people who actually know what they're talking about. They hit every single feature I'm looking for as a developer.
Summary: Pantheon is a website platform, not a simple hosting environment. Some of the features are nearly magical, and the others are all on the wishlist I've had for my sites for years. I wouldn't believe it existed if I didn't use it! Check it out!
Migrate a site you have that gets a ton of traffic and look at the performance difference. It's worth taking the extra time to test no matter what platform, but with Pantheon, I was more than pleasantly surprised with the result!