For both public and private offerings, IaaS tends to be the current dominant delivery model. When enterprise CXOs think of the cloud, they think in terms of data center infrastructure being delivered in a similar fashion to the way they work today. The names that come to mind are familiar providers such as Amazon and Rackspace. One of the reasons for this is that IaaS is the closest delivery model to current data center architecture and, as such, provides a sense of familiarity and trust, as well as a less disruptive migration path.
Many options exist for delivering IaaS in the private cloud, with a large investment from several industry leaders to advance those technologies. VMware's vCloud Director offers IaaS capabilities to VMware environments, while organizations like OpenStack.org and Eucalyptus are building out open source frameworks capable of layering automation and orchestration onto existing virtualized environments.
The other option for private clouds is PaaS. The migration to PaaS can be more challenging because applications will need to be modified or rewritten for the chosen PaaS architecture. The advantage of PaaS architectures is that applications will be written directly onto the cloud platform, breaking them away from the one-app, one-OS, one-server siloed model most exist in today. This allows the application to benefit from the full flexibility and scalability of the private cloud architecture. Various PaaS options exist for private clouds, including Windows Azure appliances and VMware's Cloud Foundry.