I2C is to serial comms as a horse is to a car. The I2C is much faster, way more expandable, & offers a lot more options. You could easily put a hundred devices on the I2C bus, but that would be a challenge with serial comms. It's also easy to do circuit boards for I2C devices (a plus for me since I'd rather be fishing).
Attached are the schematics for the Picaxe-20M2 board & joystick DIO board used on this project. As you can see, there ain't a whole of lot of complexity.
Have a fun day!