Show us the code and wiring you used for the 3 devices and provide links to the datasheets of the parts.
There is no relevant difference between the I2C on the UNO (ATmega328) and the Mega (I guess a ATmega2560). The I2C devices I have work with both of them using the same code but of course there are differences in details because the two boards are different. The capacity of the two solutions may be slightly different, so without external pull-ups you might get different results.