What are the performance benefits of segregating database objects into different tablespaces?
Minimal performance benefit, the only benefit in this regard is from reduced fragmentation. But Oracle and most filesystems handle this much better these days than in the past; Oracle handles this better with "automatic segment space management" and the Oracle "filesystem" ASM, though you don't need to use the latter.

It's more a manageability choice these days; personally I wouldn't bother with separate tablespaces, but I do often create one per application. This allows you to use a transportable tablespace export if you so desire.