There is a difference in the amount of health benefits between filtered/hot brewed coffee and cold brew coffee other than the temperature. With cold brewed coffee it retains the healthy oils in the coffee that carry the antioxidants and most benefits such as reducing inflammation, protecting against disease etc. During the brewing process the healthy oils are caught in the paper filter and don't reach your cuppa java, meanwhile french press and cold brew both are unfiltered and you are able to benefit from the oils.
Some benefits According to studies by John Hopkins University of Medicine:
*regular and decaf coffee have a protective effect on your liver. Coffee drinkers have a healthier range of liver enzymes than non coffee drinkers.
*reduced risk of colorectal cancer by 26%
*reduced risk of strokes in women
*reduced risk of Dementia and Alzheimer's disease
*increases strength of your DNA strands (important to prevent cancer, tumours)
*reduced risk of Parkinson's disease, also increases control of movement in Parkinson's disease
*ward off heart failure when your heart has weakened ability to pump blood
less chance of type 2 diabetes and helps your body process blood glucose better