For the vast majority of them, rented servers at a managed hosting provider would beat cloud in price hands down, but for some the difference might be small enough once they've actually optimised their cloud setup that it's a judgement call. I usually recommend clients plan for optimizing their cloud setup first, both to get a fair comparison and also because a lot of the assessments you need to do of your cloud environment to do that will also make it easier to figure out what you'd pay for a managed hosting setup as well (e.g. understanding base load vs. spikes, durability requirements for different subsets of storage etc.)

For some of them, a colo facility would be cheaper, but that's highly dependent on where you want to host it (e.g. I'm in London - putting things in a colo in London is really hard to make cost effective vs. renting servers somewhere with lower land costs; data centre operators are real-estate plays)

However, you can usually make managed hosting/colo even cheaper by sprinkling some cloud in. E.g. a "trick" that can work amazingly well is to set up the bare minimum to let you spin up what you need to handle traffic spikes in a cloud environment, and then set up monitoring for your load balancer so that you start scaling into the cloud environment once load hits a certain level, but use only the managed hosting below that level.

That way, you almost never end up actually spinning up cloud instances, but you gain the ability to run the managed hosting environment far closer to the wire than you could otherwise safely do, and drive your cost per request down accordingly.