Ultimately it's about preference in taste and preference in process. Some people will prefer French Press while others swear by Chemex.
The Chemex brew method can absorb oils, mainly with paper filters. Reusable filters tend to allow more oils through for a bolder taste. There's also a further level of control with this brewing method. Your pouring technique, how you bloom the grind etc. all gets taken into consideration with the final brew.
The French Press brew method mainly leaves you with a fuller cup of coffee when compared to the Chemex. It can be richer, again taking into consideration the type of coffee you're using, grind size, and the effort you put into the press itself.
