By definition, the most difficult market conditions for trend-followers are when there is no trend to follow. By contrast, contrarians can use those market conditions to good effect, using support and resistance levels as turning points, whereas a strongly trending market could cause them problems.Some traders use more than one system depending on the prevailing conditions. Others know when the market will cause whipsawing and an erosion of capital, and will therefore go to a cash position.(I am assuming here that we are not including very short term/intra-day trading).
Trend followers can either follow the example of Bill Dunn (a prominent trend follower profiled in Michael Covel's book Trend Following) - he utilises a system that is always in the market long or short, and as he says "rides the bucking bronco" - or you can have your system determine when the market is not trending, which will enable you to sit on the sidelines.
Contrarian traders, those who try and catch market turns etc, will struggle in a strongly trending market . I myself once utilised a very simple system based on hourly charts that tried to catch market turns on the major indices. It did phenomenally well over a period of 2 - 3 months, before I suffered a dramatic change in fortunes. Why? Because the market conditions had changed. My success had come during a consolidation period in the markets. Once a clear trend had became apparent, I had no plan in place to counteract that.
So, you need to ensure that either a) your method will work on all kinds of market environment, or b) your method ensures that you are out of the market in those 'difficult' periods.