It seems there's a rather vocal group of users on the official Saints Row: The Third forums and the official Steam threads for the game having major performance issues in outdoor areas. This is a problem, given that the open-world parts of open-world games tend to, you know, be in the open areas of the world. Outdoors.
The performance problems appear to be spread across AMD and Nvidia hardware. Volition is soliciting users for their configurations and dxdiag files (don't ask!), and is working with with the GPU manufacturers on possible solutions. Having perused some of the message board threads in question, a more common configuration aspect for those affected is an overclocked CPU or GPU, which can cause negative performance issues on certain titles. Meanwhile, Volition has stated that it's still looking into the issue, one patch later.