It turns out both movies are the same and also different. Both movies are spawned from books by the late Donald Westlake. Payback was adapted from the novel The Hunter published in 1962 under the pseudonym Richard Stark. The movie Parker is based on the Westlake book Flashfire
The two plots are incredibly similar. Flashfire was published in 2000. This quote is from Amazon -
In Flashfire, Parker’s in West Palm Beach, competing with a crew that has an unhealthy love of explosions; when things go sour, Parker finds himself shot and trapped—and forced to rely on a civilian to survive.If you know anything about Payback you can easily confuse the two plots.
I might see Parker but only because I like Statham as an action actor. He's real and believable. But if you're interested in this story and want to see some world-class acting from Hollywood's best you must see 1967's Point Blank with Lee Marvin, Angie Dickinson and Keenan Wynn. Here's a quote from IMDB
Without delving into psychology or motivation, the film places emphasis on action and surface appearances, superbly capturing the glossy, depersonalized feel of a 1967 Los Angeles--a nightmare landscape of concrete, glass and coiling freeways.Marvin is icy cold and so believable as a killer. Dickinson is sexy but hard-as-nails. The film is in color but is shot in a film-noir style. Don't see Parker or Payback without seeing the stunning original, Point Blank.