Two wire vs. three wire serial interface for RTC
The main difference between SPI (3-wire interface) and I2C (2-wire interface) is, that you have to send an address when using I2C. So it won't be as fast as SPI because you have to send more data.

When using SPI you will need an extra pin for the chip enable signal.
This will be required for each slave. So it's faster, but you need more output pins.

I would prefer I2C because speed doesn't matter in this scenario.

The ATMega microcontroller has hardware peripherals for both methods so it's up to you