What is a public cloud?

A public cloud, as it is clear by its very name is a cloud service that is open and allowed to multiple clients by the cloud service provider. The public can easily access and enjoy the unique features of cloud environment on a public cloud. Public cloud includes SaaSPaaS, and IaaS services.

What is private cloud?

Private cloud promises complete privacy in the cloud environment.  Private cloud does not share services with any other organization but the actual cloud user enjoys himself.

So before deciding which one works best for you, let’s have their difference of features, benefits and usage. 

Public cloudPrivate loud
It is a shared computing cloud service among different customers but the data and applications of each customers remains safe and can’t be seen by others.  It is an unshared offer where all the services and application of the cloud are dedicated to a single organization. It is the goal of the private cloud to satisfy the demands of a single tenant.
In public cloud, the cloud providers offer a variety of IT services and resources to the public where they pay for what the resources they use.  In private cloud the organization does not share the applications and resources with the users. Though the information can be hosted in their own preferred way.
It is the cost effective solution to access the desired data. But as it includes compute, storage, databases, analytics, networking, mobile, management tools, security and enterprise applications where the selection of required application becomes really hard and the organization is more likely to purchase some extra services which it might not use at all not even in future. So in such cases they have to pay more than necessary.      The private cloud solution will certainly decrease the usage and server load through which the cost will reduce without affecting the quality performance. If the service provider is unbiased and have spent time in understanding your business requirements, he will suggest you the most cost effective solution suited your business the best.   
It is no doubt super easy to get enter in the cloud just by having the internet connection.  In a private cloud, all services, resources, software and hardware work on a private network thus are exclusively accessed by a single company.
In public cloud service all the resources are in the control of the third party, it operates all the servers and manages the storage options and provides network access to the public if they subscribe the same cloud.  The private cloud services can use the infrastructure and resources present in the organization’s on premises data center but some tenants also prefer to have new and separate setup provided by a third party organization.   
It is highly scalable and flexible even with a large number of users.It is open for the single tenant environment thus scalability is not the issue.
It works best for archival, on demand hosting, auto scaling environment, companies having a large number of users and for different research institutions.  It is mostly preferred and considered ideal for the companies which need complete security and need advanced flexibility and adaptability for hosting business data and applications.