Last stayed at the Conrad was 5 years ago. Now I do mostly Marriott. Both places are great properties. Location being the same. It boils down to which place will you most likely get upgrade. I think your chances are better at the MR (being plat vs gold for HH). I had pretty good luck with MR. Keep in mind things could change a lot in 5 years. I love the c lounge at the JW.
I am sure others will give you a more detailed eval.