In most contexts, they say essentially the same thing: The work will be finished tomorrow.
You can say it either way because there is often more than one way to express the completion of a task:
- You can be done working on a task
- The task can be complete
In cases where one individual is working on a task, both of these become true at the same time.
You can change the generic "my work" with a more concrete phrase to see how this works (each sentence in the pair is grammatical and acceptable):
I'll have finished the new roof by tomorrow.
I'll be finished with the new roof by tomorrow.
I'll have finished designing the interface by tomorrow.
I'll be finished with the interface design by tomorrow.
I'll have finished stripping the paint by tomorrow.
I'll be finished with the paint stripping by tomorrow.
I'll have finished doing my taxes by tomorrow.
I'll be finished with my taxes by tomorrow.
All of these assume that the task is being completed by a single individual. Other circumstances may apply:
I'll be finished with the wiring on the Simpson house tomorrow. Then I'll start working on the Flanders house, while the rest of the crew will finish the wiring at the Simpson house.
In that last example, me being done with the task does not mean the task is complete – it simply means I am no longer contributing to the project.