This is a false dichotomy. There's no need to flip to colo, when dedicated hosting exists. The provider takes care of the network, hardware, and potentially much more depending on the service agreement. You can even have the provider setup a cloud environment for you, if you want to be able to spin up and down VMs. This eliminates the capex costs, while having much lower opex costs than colo at smaller scale.

Considering that you can easily do dedicated for 1/7th the cost of Amazon for the equivalent amount of resources, it doesn't take anywhere near 150 machines to realize cost savings, it's more on the order of one complete physical machine as a dedicated server. You can purchase a 2nd one for redundancy and/or for always available additional capacity, so that you can burst to double your usual peak performance and still save 5/7th the costs of Amazon. If you're expecting to require the ability to scale much higher than 2x, you can also purchase a bunch of servers just for 1 month, or even less time depending on the provider, or take a hybrid approach if you really need an extreme amount of dynamic scalability. The reality though is that such extreme scaling is in the minority of cases.

I'm not sure how you arrived at the 150 machines number, but that sounds like 3-4 full cabinets and about right to have a reasonable scale for colo.