Both the 3910 and 82G71 vacuum cleaners are designed to work on carpeted surfaces. The 82G71 vacuum has added components to help it clean other surfaces as well, including upholstery, bare floors, low pile carpet, stairs and automobiles.
Both Momentum series vacuum cleaners are cyclonic, upright and bagless, and they utilize HEPA filter systems. The 3910 has a 35-foot power cord, a permanent belt, a style 7/8 filter and a rotating brush. The 82G71 has a 30-foot cord, a style 7/9/10/12/14/16 replacement-type belt, a pre-motor foam filter and two rows of rotating brushes. The 82G71 also comes with a carry handle, a headlight, a soft bumper, an easy-empty dirt container, an airflow indicator and dual edge cleaning capability, which the 3910 lacks.
Both the 3910 and the 82G71 come with a variety of attachments, including crevice tools and extension wands. While the 3910 has a basic dusting brush as well, the 82G71 has a combination dusting and upholstery brush and also a TurboBrush.
Bissell no longer produces the 3910 series. You might be able to find one for sale used from vacuum retailers, resale shops or online. The 82G71 series, as recently as June 2011, was available for purchase new directly from Bissell and was for sale at stores including Kohl's and Kmart for about $100.