There is no complete data on violent crime rates for the two administration periods. Regulations for recording crime have also changed in this time.
Under the Federal Bureau of Investigation's (FBI) Uniform Crime Reporting (UCR) Program, four offenses comprise violent crimes: murder and non-negligent manslaughter, rape, robbery, and aggravated assault. Also, "violent crimes are defined in the UCR Program as those offenses that involve force or threat of force." According to the FBI data, the highest rate of violent crime under Barack Obama's term (2009 to 2017) was 431.9 per 100,000 inhabitants. However, there is insufficient data in relation to Donald Trump's administration (2017 to 2021). The last available updated data is from 2019, which was at 366.7 per 100,000 inhabitants. Further, the table indicates that rape was added under the revised definition from 2013 only, and there is no record of arson data in this table.
According to the reports published by The Marshall Project and Vox in 2019 and 2020, aggravated assault and murder, both listed as serious violent crimes, have risen since 2018. The Washington Post reported in September 2020 that “the number of violent crimes per 100,000 population was nearly 16 percent lower in 2016 than in 2008, and the property crime rate dropped nearly 24 percent. But the murder rate didn't drop at all — it was 5.4 per 100,000 both in 2008 and in 2016."
In 2020, the Council on Criminal Justice (CCJ) published a report named "Impact Report: COVID-19 and Crime" and said that the killing of George Floyd by Minneapolis police, in addition to COVID-19, had contributed to a rise in crime rates. The CCJ noted that during the period of recorded data (January 2017 and June 2020) “not all of the cities reported data for each crime, and offense classifications varied somewhat across the cities."
Complete data regarding violent crimes from both administrations are not available for comparison. Updates and changes have taken place to regulations on recording crime. According to the FBI data table, the rates were adjusted for 2018. Further, the reports suggest there was a spike in rates during the Trump administration, but also that there wasn't a significant drop during the Obama administration.
Therefore, the claim that violent crime increased during the Trump administration compared to the Obama administration is unverifiable.