The Brooks Addiction is a motion control stability shoe that is tailored towards walkers and runners with significant over pronation.
As with other Brooks comfort shoes like the Beast, the Addiction features Brooks' BioMoGo DNA midsole for maximum cushion and dynamic support (depending on how much pressure you put on it).
However, the Beast is more tailored to over pronators because it features the Progressive Diagonal Rollbar in the midsole. If you aren't sure about your own level of pronation, it would be wise to visit your local run specialty store for gait analysis before buying the Addiction. But, if you do have over pronation issues, then you won't find a better walking and running shoe to meet your needs.