I have the Fiesta ST and I used drive the previous generation Si (K20 engine). I absolutely love the Fiesta ST but there are things I miss from the Si.
My thoughts for each category:
Exterior: Fiesta ST
Purely subjective of course. I don't like the bulbous look of the new Si.
Interior: Push
Both have cheap plastics but the interior layouts are ergonomic.
Driver Comfort: Civic Si
Recaros are nice but the Civic Si's seats are nice too. The pedal and shifter positions are more natural in the Si. The Fiesta ST's shifter is quite low. The pedals are more centered in the Civic Si.
Passenger Comfort: Civic Si
There is a lot more room in the Civic.
Audio System: Civic Si
The Fiesta ST has a decent system. The Civic Si has an amazing little 8" open-air subwoofer, which doesn't sound like much, but makes a big difference.
Engine: Fiesta ST
The current K24 is not as fun or exciting as the Ecoboost 1.6L. The K20 had a lot more character. Reving up to VTEC is quite addictive. The torque plus the turbo sound makes the Fiesta ST quite special.
Transmission:
Civic Si
The Honda 6-speed is legendary. Shift action is direct and buttery smooth. While the shift action in the Fiesta ST is quite smooth and easy, it feels heavily damped and not as engaging as the Honda.
Handling: Fiesta ST
Absolutely amazing suspension setup and tuning in the Fiesta. Even the Civic Si with factory performance suspension can't match the Fiesta ST's composure. The Fiesta ST manages to control body roll while being more compliant over rough roads than the Si.
Fuel Economy: Fiesta ST
Ecoboost is quite efficient.