The Benefits of Public Cloud Computing
Simplicity and efficiency are the overarching benefits of having a public cloud. Public clouds are offered as a service, usually over an Internet connection. An off-site third party provider hosts and manages the system. Users connect to the system via web applications or services. Public clouds usually charge a monthly usage fee per gigabyte and bandwidth transfer charges.
Cost: Having a cloud computing model in place, organizations can trim their IT budgets because they don't have to purchase physical hardware (which also saves on energy costs), as the servers are virtual - hosted at a third party. Organizations can customize their clouds with specific storage parameters, applications, and security options so that they only pay for what they need. Since the cloud is hosted by a third party, the organization doesn't need to spend money to have an employee monitor the system; it is taken care of by the host.
Time: In house servers take time to maintain. If hardware or software configurations need to be altered, or if a server crashes or needs to be restarted, the process can often take a couple of hours or a couple of days depending on the situation. With cloud computing, because everything is virtualized, reconfiguring the cloud takes minutes.Also - because the servers are hosted on the cloud, if one server fails, another can instantly be activated, reducing down time.
Maintenance: Due to the fact that the public cloud system is hosted off site, internal employees are not responsible for maintaining the system. The design lets users update or introduce technologies into the system at a much faster rate as everything is managed at the host company. Having a virtualized public cloud means never having to deal with a physical server; it can be maintained from a simple configuration screen.
Disadvantages of a Public Cloud
Lack of Control: Due to the fact that third party providers are in charge of storing and maintaining the data systems, many feel as if they don't have enough control over their personal data.
Speed: Public Clouds are based on internet connections, meaning the data transfer rate is limited to that of the Internet Service Provider (ISP), which is usually no more than 10mbps. If an organization is storing and transferring large amounts of data (high definition video for example), a public cloud may not be the best bet.
Lack of Investment: Although a great cost saving method by reducing the need to invest upfront, renting the service from an outside provider also means that there is little capital gained. Having items such as servers and network equipment can pay off in the long run as assets and tax advantages.
The Benefits of Private Cloud Computing
Private clouds are built from software that runs on a piece of hardware at the organization. The difference between a public cloud and a private cloud is that a private cloud is controlled by the organization. The benefits of this system are that although an investment due to the fact hardware is required, it costs considerably less than traditional data management systems. The cost savings is due to virtualization in which one physical server acts as host to several virtual servers, each of which runs on a layer of software.
Control: Due to the fact that the hardware is on-site, organizations have more control over their data. The organization is in charge of monitoring and maintaining the data giving them complete oversight of their data.
Performance: The private cloud is deployed inside the firewall on an organization's intranet, meaning that transfer rates are dramatically increased. Read access off of private clouds can be as fast as 100mbps, or even more if the organization has a gigabit Ethernet connection. Storage capacity is also higher with a private cloud. Private clouds usually start with a few terabytes and can be increased by adding additional disks.
Disadvantages of a Private Cloud
Cost: Private clouds are more expensive than public because they require both hardware and maintenance personnel. To build a private cloud, an organization needs to invest in hardware or use already existing systems whereas a public cloud is all handled off site. Private clouds also require system administrators. However, one system administrator could easily manage a 100-node cloud with a part-time effort. 
Maintenance: Since the private cloud is hosted on sight, the organization needs to provide adequate power, cooling, and general maintenance. The host organization also runs the risk of data loss due to physical damage of the unit (i.e. fire, power surge, water damage).
 "Seeding the Clouds: Key Infrastructure Elements for Cloud Computing." IBM. Feb.2009. IBM Corporation. 26 Feb. 2010. <http://www-935.ibm.com/services/in/cio/pdf/oiw03022usen.pdf>.
 Fogarty, Kevin. "Cloud Computing Definitions and Solutions." CIO 10 Sep. 2009.Wed. 27 Feb 2010. <http://www.cio.com/article/501814/Cloud_Computing_Definitions_and_Solutions>.
 "Cloud Computing Public or Private? How to Choose Cloud Storage." Sys-Con Media. Sys-Con Media, 2008. Web. 26 Feb 2010. <http://www.sys-con.com/node/707840>.