Both are single-client server services hosted on identical, powerful, reliable, and high-performance hardware.
The administered version is provisioned with CentOS and Plesk. If you are a hosting reseller, you might prefer the managed version due to the robust reseller features of Plesk.
The Developer version offers a choice of Ubuntu, Debian or CentOS operating system on a single server without a web control panel. A VPS Developer allows you to install and configure the stack on top of the operating system according to your needs. If you need a highly customized or unique LAMP / Application stack, or want Ubuntu or Debian, then the developer's setup would be better for you.
Note: Linux command line skills are required to manage a Dedicated VPS Developer.
