In the case of a Linux operating system, running with different partitions, and different types of partitions improves performance. This is because the different types of partitions are used for different purposes.
In the case of generic partitioning, where all the partitions created use the same file system and are used for storage... where you partition just to make organizing things easier... it's all about personal choice. It is possible to make a hard drive work harder (IE shortening the life slightly or decreasing performance) depending on how you write to and from the partitions on that drive. No, I'm not saying that this is always the case.
Is there any real benefit? It can help you organize what you use the drive for better.... depending on how much help you need organizing. Let's say you were going to use the secondary drive for your time machine backups instead of the external drive. Creating a partition on the secondary drive just for Time Machine to use isn't going to improve performance or make Time Machine do it's job better. It just means you will tell Time Machine to save the backups to a "drive" rather than just a directory. Semantics, in this case.
Really... it depends on whether or not you feel the need to have that level of organizational compartmentalization. Some do, others don't. So the benefit is to your peace of mind.