I've seen several large-scale cloud migrations and the bill has always been higher, usually egregiously so. In one case in particular, we would've been able to re-buy all the (perfectly adequate) hardware in our racks every 45 days if we had been pouring the cloud spend into hardware.
In another case, I've seen a company that spends dozens of thousands of dollars a month on the cloud infrastructure to run a site that services a max of 50 concurrent users. The truth of that matter is that the production site could run just fine on any developer's laptop and a one-time spend on a pair of geographically-dispersed dedicated servers would free up huge amounts of cash without any measurable/actual impact, but the bosses won't feel very important if they acknowledge that. It boosts their self-image to have a big cloud bill and feel like a grown-up company because they're paying big invoices, and plus the CxOs can prance around and tell everyone how forward-looking they are because they're "in the cloud".
It seems like the most common pitch is "cloud is usage-based billing" and people operate under some vague theory that this will translate to savings somewhere, but despite popular belief, most workloads are reasonably static and you're just going to pay a lot more for that static workload.
The fantasies of huge on-demand load are mostly a delusion of circular self-flattery, aggressively pushed by rent-seekers and eaten up all too eagerly by people who are supposed to be reasonable stewards and sometimes even dare to call themselves "engineers".
By all means set up the cloud stuff and have the account ready to take true ad-hoc resource demands, but the number of cases where AWS and friends are an actual net savings over real hardware is infinitesimal. Most companies would be much better off if they invested in owning at least the baseline 24x7 infrastructure.
I guess the issue there is that since most companies don't really have the dynamic demand they imagine, if they actually used cloud providers for elasticity, they'd almost never use them and then they couldn't feel cool enough.
If you're a random guy, it's going to be cheaper and better to run on a Linode or small AWS instance than it will be to rent and stock a rack. If you have more than 5 employees, this is almost certainly not true.