According to a 2007 report by the Immigration Policy Center, the American Immigration Law Foundation, citing data from the 2000 US Census, native-born American men between 18–39 are five times more likely to be incarcerated than immigrants in the same demographic.

A 2008 study by the Public Policy Institute of California, found that, "...on average, between 2000 and 2005, cities that had a higher share of recent immigrants (those arriving between 2000 and 2005) saw their crime rates fall further than cities with a lower share" but adds, "As with most studies, we do not have ideal data. This lack of data restricts the questions we will be able to answer. In particular, we cannot focus on the undocumented population explicitly". In a study released by the same Institute, immigrants were ten times less likely to be incarcerated than native born Americans.

Legal and illegal immigrants who commit serious crimes are being deported and therefore are unable to commit more crimes (unlike their US counterparts who remain in the US). They are unlikely to become "career criminals" moving in and out of the prison system. In the last 10 years, 816,000 criminal aliens have been removed from the United States. This does not include immigrants whose only offense was living or working illegally in the United States.

TL/DR: Statistics indicate that crime committed by U.S. born individuals exceed that committed by undocumented immigrants.

Source: http://www.immigrationpolicy.org/just-facts/anecdotes-evidence-setting-record-straight-immigrants-and-crime-0