What are the benefits of using Fastly versus simply having my own self-hosted Varnish? Are there additional benefits and features that Fastly provides that regular Varnish does not, or is it simply that Fastly is managed Varnish in the same way that CloudAMQP is hosted and managed RabbitMQ?
I just stumbled across this question, I know you asked this a while ago but I'm going to try and answer it for you regardless.
You are correct in assuming that Fastly manages the Varnish instances for you, so you don't have to deal with manually managing your servers. It is a slightly different concept than CloudAMQP however; CloudAMQP is a managed RabbitMQ system that lives in a specific datacenter, perhaps with Multi-AZ enabled for failover purposes.
Fastly is a full blown content delivery network which means they have machines running Varnish all over the world which could significantly increase your user's experience because of lower latency. For example if an Australian user visits your website he will be retrieving the cached content via Fastly's Australian machines, whereas if he were to connect to your own Varnish instance he'd probably have to connect to an instance in the U.S. which would introduce a lot more latency. On top of that it wouldn't only improve speed, but also reliability. Your single Varnish instance having a failure is quite likely, Fastly's global network of 1000s of machines running Varnish collapsing is very unlikely.
So to sum it up for you:
Regards,
Rene.