Which sentence is correct?
My project is dependent upon your project completing.
My project is dependent on your project completing.
Which sentence is correct?
My project is dependent upon your project completing.
My project is dependent on your project completing.
They are equivalent; upon is just a more formal term for on, and it is especially used in abstract senses.
The NOAD reports the following note about the usage of upon:
The preposition upon has the same core meaning as the preposition on. Upon is sometimes more formal than on, however, and is preferred in the phrases once upon a time and upon my word, and in uses such as row upon row of seats and Christmas is almost upon us.