Not matter which software you used, basically the same result should be produced. If the two tools generated different results based on your data, the only way to do is to check your data.
Well, QTL cartographer has been used for many years and is widely accepted. You may first use QTL cartographer and evaluate if other tools are appropriate for your work.
Apply software as per your requirements. if your objective is some highly variable trait QTL cartographer can a better choice for getting the extent of variation explained by each locus. If you are still getting complexity in your results you may try ICIM or others.
I think both are reliable software's for mapping QTLs. As i used both the software's for mapping , got similar results. Check your data once like input data files
It is recommended that if your data is skewed you have to do data transformation depending upon the type of data you have (percentage data etc). You may use angular transformation methods for the transformation. Once after you finish data transformation you may use the data for the QTL analysis.