Hi Tanja,
Keep in mind that the Adword Keyword tool is meant for advertising, so the "competition" is thought to be a better measure of paid competition, not the organic rankings you are trying to achieve.
The best approach is to use the KW difficulty tool to analyze the competition. Look at all the metrics. Run a complete report for your top keywords. Are the competitors pages properly optimized? Can you beat them anywhere? Pay close attention to title tags and inbound anchor text, as these carry a lot of weight.
I still get most of my ideas from Google's tool, at least as a starting point. I then try to find modifies that I can more easily rank for. There are 3 types of modifiers I can think of off the top of my head:
Let's use the keyword "running shoes" for example:
Type Modifier: "Wholesale Running Shoes"
Location Modifier: "Running Shoes Germany"
Date Modifier: "Running Shoes 2012"
By optimizing my page around specific modifiers (and you often can't find these in Google Adwords) you can rank more easily for given keywords. The more specific, the better.
