I've heard rumors that Mega has a higher precision, though I do not understand how this can be true if the scale of analogRead is still from 0 to 1024.
How can I argue for use of digital data-over-I2C (13-16 bit data) versus analog accelerometers from the ADC standpoint?
No it's false.
As for every AVR you can enhance the AtMega328p ADC resolution. See Atmel Application Note : AVR121.
Uno board is for initiation only, she does it well, it was not expected for professionnal use.
I don't know the Mega layout but Uno layout is very poor concerning analogical signals.
No analogical ground near A0-A5 pins, the layout of Aref line is an horror : I have to sold 100nF capacitor directly on the micro socket to have stable measurment, and so on ............
How can I argue for use of digital data-over-I2C (13-16 bit data) versus analog accelerometers from the ADC standpoint?
I'd vote on digital-over-I2C, just note arduino has slow I2C < 400kHz
I'd go with digital over SPI, much faster.
Here's a simple chip to start with - 8 channels of 12 bit ADC
http://www.microchip.com/wwwproducts/Devices.aspx?dDocName=en010534
http://www.digikey.com/product-detail/en/MCP3208-CI%2FP/MCP3208-CI%2FP-ND/305928