you probably need a voltage translator (page 10 http://www.nxp.com/documents/application_note/an97055.pdf
) between the two boards.
Both the UNO and the MEGA run at 5V and so their SCL and SDA channels will take for logic level something like <0.3*Vdd is LOW and >0.7Vdd is HIGH. If you make the calculation 0.7Vdd with Vdd= 5V is 3.5V which is ok for a UNO to MEGA connection with the pull ups at 5V but it is higher than the 3.3V at which you are pulling up your lines when having the DUE to MEGA connection.
I would also suggest you to change the pullups. Rip out the one on the arduino Due (which on the schematic is said to be 1.5K but in reality is just 1K) and add an external 4.7K on both sides of the translator.