Due to my research, AMD has superior computing power compared to Nvidia, and that's also the reason the litecoin miners use AMD over Nvidia, so wouldn't it be the logical idea to create more clusters using AMD GPUs (not CPUs) and AMD has better open source support.
It entirely depends on what you are computing!
HPC clusters vary greatly depending on the tasks they maybe undertaken and the software that is running upon them. It also greatly depends upon scale-ability of the computing tasks. For example a web hosting cluster can not utilize GPUs in anyway shape or form.
GPU's work great for particular applications due to their architecture and design. GPU's are extremely fast due to the number of cores although these cores are nowhere near as powerful as a single CPU core (aka a GPU achieves computational power in numbers). However, this is only good if your tasks are highly paralleled process that are not dependent upon each other. Such as calculating hashes, you do not require the answer to a previous hash solution to compute the answer to the next.
CPU's hence work much more effectively at serial computational tasks due to their pipeline designs (as I understand). This is why co-processors, like Intel Xeon Phi, are very popular amount certain simulation tasks. Their design is more akin to CPU's whilst expanding their capabilities towards the quantity of that GPU's can compute.
So in short AMD GPU's if your application can utilise OpenCL. However Nvidia maybe desired if your application is using CUDA.
Ok I know about cuda, but wouldn't using AMD cards be a lot cheaper and more open and changeable due to openGL?
Depends on what cards you are getting. AMD doesn't really have any competitive cards for the high-end compute cluster anymore. Whilst Nvidia has cards designed for server environments with immense computational power are available. (aka the Tesla line of cards (K80))
In large scale out operations like computational clusters, money is not usually an issue. Getting as much performance in as little space possible is the goal and also using as little power as possible.
I mean a cluster that you could be running out of your home for no apparent reson or you want to set up a cloud based VM service or something like that