I've got both gauges. Mine are in 1100s though not in the 870. I've got an older Sporting Clays model 28 with the 25" barrel and a 20 in the "Light 20" model, that's not all that light.(7lbs 70z) The 28 is about 8oz lighter. I'm sure an 870 in either gauge would be lighter than an 1100 but as to the 870s respective weight difference per gauge I don't know.
I use them both for quail and chukar and my wife occasionally uses the 28 for skeet. They work fine for both. I don't reload though and when the two flats of 28 gauge ammo I have left are gone I'll probably just shoot the 20. 28 gauge ammo is twice as expensive. To me there's not enough weight difference to justify the difference in ammo cost and the 20 is more versatile and at least as effective or more.
