Eco is different to City, but you'll either have one or the other.
City on just makes the steering lighter
Eco on makes the steering lighter, and reduces engine power to help improve fuel economy (apparently) but some question how effective this is, as if you want to go faster you then need to plant your foot more, which uses more fuel.
Eco mode is only available with the TwinAir engine -- it basically reduces torque and makes steering lighter. On Dualogic cars, it also tends to hold on to higher gears longer before downshifting, so it's more fuel efficient that way. Eco mode reduces your ability to accelerate quickly.