the H3 geometry on a 56cm frame has a 1.5 cm longer head tube, a .6 cm shorter top tube and a .2 degree slacker head tube.

the handlebars will be that much higher and closer to you putting you in a more upright position than on a H2 for the same stem length/angle.

that's the difference. if you don't know what anything i said means, just get the H3. if you can get the frames for the same price and you want a more upright position i don't see why you would want an H2.