Private prisons internationally seem very similar to ones here. The GEO Group has arguably the largest international operation, and a company called Serco operates a few as well. But nowhere else in the world has such extensive privatization as we do here in the US. Regardless, they still certainly have their issues.
For one, they don't staff their facilities nearly to the same levels as government-run ones. This leads to increased levels of violence, increased incidences of escape, and a more dangerous situation for guards and prisoners alike.
They also hire a lower quality of staff than government-run prisons. Like staff who secretly watch female prisoners undress.
But most similar of all is the complete lack of transparency and oversight of private prisons abroad. As is the case here, private prisons aren't subject to open records/sunshine/freedom of information laws that government agencies must abide by. Because they're private corporations, they claim nearly all aspects of their operations are trade secrets, and thus decline to disclose information on things like staffing ratios, incidents of violence, etc.
The Australian Senate recently found that, despite paying Serco $1 billion to operate a private immigration detention center, "The Department of Immigration and Citizenship collects scant data on breaches and has limited knowledge and oversight of staff training levels." Great.