From my limited experience, the cloud is always more expensive if you know your exact usage requirements. If, for example, you know that six octo-core 16 GB RAM, 512 GB SSD-in-RAID1 servers would fit your needs from now until 10 years from now, you will do better to just rent them from SoftLayer, Hetzner, etc.
However, if you anticipate growth, or need to be able to spin up a test server, then shut it down a day later, etc. then you are better off paying premium for the cloud. Sure, there are economies of scale at play here: AWS has so many servers, they are not paying a person to log into every one of them every so often to run updates, etc. However, make no mistake: everything you would have to do with a server, Amazon has to do too. In fact, they have to do much more to keep all of them running at once. That cost will be passed onto you.
Even with all of that, it's cheaper if you want to be able to spin something up, then shut it down. Another great example is the additional services provided by the likes of AWS: you can get things like load balancers, cache servers, database servers, orchestration services, etc. You can do all of this yourself, but at some point it's cheaper to just pay for something like ELB than to learn how to do it yourself and spend the hours to set it up. Human time is more expensive than that.
Lastly, if you just need a really small machine, there is no beating the cloud. You simply cannot get a dedicated machine for $5/month, and you likely never will.
I found OVH's dedicated server offerings to be so cheap that there was no point in using shared hardware for the flexibility. Then again, I'm not running my entire business on these boxes... but I don't think I'd have a major issue if I wanted to!
However, if you anticipate growth, or need to be able to spin up a test server, then shut it down a day later, etc. then you are better off paying premium for the cloud. Sure, there are economies of scale at play here: AWS has so many servers, they are not paying a person to log into every one of them every so often to run updates, etc. However, make no mistake: everything you would have to do with a server, Amazon has to do too. In fact, they have to do much more to keep all of them running at once. That cost will be passed onto you.
Even with all of that, it's cheaper if you want to be able to spin something up, then shut it down. Another great example is the additional services provided by the likes of AWS: you can get things like load balancers, cache servers, database servers, orchestration services, etc. You can do all of this yourself, but at some point it's cheaper to just pay for something like ELB than to learn how to do it yourself and spend the hours to set it up. Human time is more expensive than that.
Lastly, if you just need a really small machine, there is no beating the cloud. You simply cannot get a dedicated machine for $5/month, and you likely never will.