Cell fracture on an object products rigid bodies with different shapes/meshes. I was wondering if it was possible to assign particles to have different objects, rather than a single object applied to all particles?
Yes, they can. And yes, it is. ;-)
One way is to render a group of objects, rather than just one object.
If you create a group, you can assign that group in the particle settings of your emitter. By default, it will randomly choose one item from the group each time it creates a particle. But there are some other settings where you have a little control over how it chooses.
To create a group, select several objects and use the shortcut CTRLG. That will group the selected objects together. That group will have a name that you can use in the render section of the particle settings on the emitter (shown below).