The HMC is a single console from which you can manage multiple systems.  It is addressable on your network with a browser session from anywhere on the planet.  If you can get into your network you can get to your systems.  You can even powerdown the Power i and bring it back up from your family room if you want.  This includes IBM being able to get to your system when necessary, including their being able to put system modules into debug when necessary to work on APARs and PTFs for your benefit.

From the HMC you have total access to all parts of your hardware and operating system.  You can take over the console for any of those systems all from the single HMC.  You can create and managed logical partitions and re-IPL them individually.  You can also manage the operator panel for each system remotely.  You also have control of Capacity on Demand features from the HMC.

Much more can be found in the IBM Power Systems HMC Implementation and Usage Guide online.

It's been awhile since I had to look at this, but there are (or were) certain partitioning capabilities that are only available through HMC. Also, larger servers require (or at least used to require) HMC; PC console was not an option. If you're not in one of those situations, by all means save the money and keep using PC console.