The HCHII and Prius get virtually equal fuel economy. If you look at the data on this site, the averages are only 1 mpg apart. The biggest factor in fuel economy is how you drive the car. Both cars are capable of getting around 60mpg if you take the time to learn how to drive them.
I find it much easier to get higher FE with the Honda that with the Prius in the city. On the highway, they get virtually the same FE.
The Prius is basically an electric car that uses the gas motor to generate additional power when the batteries can't handle the load. The Honda is the opposite - a fuel efficient gas car with electric assist. Both cars achieve their goal, high FE, through opposite approaches, but both work and work well.
In city driving, the Prius runs on the electric motor up to about 35
mph and normal acceleration but the gas engine does come on at about 5
mph (with the a/c on) to supply power, along with the battery to the electric motor unless you are really really really light with the throttle (granny style). The Prius takes about 3-4 miles to warm up. FE is poor until then. The Prius requires very careful positioning of the gas pedal in order to 'glide'.
The Honda gets high FE even when the engine is cold and is much easier to maintain high FE in the city (on level roads)
The Prius has more of a 'Cadillac' ride, the Honda more firm and 'sporty'. The Honda is definately more noisy (road noise).
If someone were to ask for a recommendation, I would have to say driver each one for about 1/2 to 1 hour and see which one handles better to them and which seat is more comfortable to them, and buy that one. I find I have more leg room with the Honda. Many Honda owners have complained about the Honda seat comfort. I think the Prius has a little better lumbar support. The Honda is also about $5k less expensive.
Hope this answers your questions.