If you are:
a) small size, at 100–200 vps
b) need a powerful but cheap resources
If you need a small cloud or test environment, with good computing resources and for little money — a private cloud will be easier and more profitable. Both in terms of capacity and price.
So, I think, that private cloud has no competitors. The cost of public cloud will be several times higher than the cost of a private cloud.
Also, the public cloud has its own peculiarities. For example in the Google Cloud you can not change something serious in a virtual machine without shutting down or re-create it. What you will not encounter in a private cloud.
Therefore, the choice is not so simple.