Where I work it is rare for me to see anyone doing any serious biochemistry (e.g. thermodynamics, kinetics...). The biochemistry will help you understand a lot of the background fundamentals on some level but all that is really necessary to do the job (at least in my bioinformatics position) will be covered in the general biochemistry introduction that often accompanies a molecular biology degree.

My assumption here is that you are going towards "typical" research position involving basic research or human research. Having a better understanding of the system as a whole (cell bio, development, embryology, genetics) will often serve you better as you don't have to learn all of that from scratch and can instead focus on the knowledge necessary for the task at hand.

Alternatively if you are going into something like proteomics or modeling the additional math from doing biochemistry will definitely help.

At many schools however the requirements for both degrees are generally very similar. The only difference in the degrees at my location is that the biochemistry degree requires more math, chemistry lab, and physical chemistry.