The goals of the study should be apparent and clear and the relevant standards should be available for testing. In fact, the method of test could be determined according to above mentioned issues.
The question does not make any sense as written (or perhaps as translated).
"Diagnosed" ? Perhaps you mean identify? If you wish to identify materials or compounds, then you will need to use appropriate methods and techniques to do so. FPLC and HPLC are both types of liquid chromatography. The phrase "better" does not apply. There are millions of possible methods to use, so you need to specify the details. No universal HPLC or FPLC method exists (That is just the name of the technique, and it does not describe a method of use). Use whatever LC method and techniques are needed to resolve the components apart and collect data on them with an appropriate detector(s). Ask your advisor to help you define your specific sample(s), goals and then research which techniques may be applicable.
You mention "crude solution". Are you purifying natural products? If so, flash chromatography is a better starting point. "FPLC" typically means "fast protein liquid chromatography".
If the crude solution is from a chemical reaction, you use thin layer chromatography plates the create a method for the flash column.
Thank you Mr. Jack Silver for your answer but my question about the diagnosing pure compounds because we cannot used these two methods with curd compounds.