While, like many statistical findings, the facts seem to be very different when examining the suicide rate differences in jails and prisons.
According to a report from the Bureau of Justice (2005), the suicide rates in jails far exceed those in prisons. According to the report, jails reported a 32.3% rate of suicide, whereas prisons reported a suicide rate of 5.8%. (The report states rates from 2000 to 2002.)
According to another report put out by the Department of Justice in 2010,
Suicide was the single leading cause of death in local jails, accounting for 29 percent of all jail deaths. Between 2000 and 2007, the suicide rate declined from 48 to 36 per 100,000, continuing a longer decline from 129 per 100,000 in 1983.
According to the same report, the suicide rates in jails far exceeded the suicide rates in prisons (general population):
Suicide rates in jails were more than three times higher than in the general population. Between 2000 and 2006, when comparable data were available, suicide was the only cause of death that occurred at a higher rate in local jails than in the general population (47 per 100,000 vs 13 per 100,000).
Regardless of the exact statistics, one can easily state that the suicide rate in jails far exceeds that of the suicide rate in prisons.