These phrases could be interpreted a few ways,
but I would say that the difference is this:
"To get an idea of something" is to get a basic understanding. You will not be an expert, but the topic will not be a total mystery to you.
For example, "To get an idea of how basketball is played."
"To get a sense of something" is more about getting a feeling about a situation.
"I am going to walk around the factory to get a sense of how the morale of the workers is."
"I visited the war zone, to get a sense of how people are coping."
These two phrases sometimes overlap, or are sometimes used interchangeably, but that is my perspective on the difference.