TL;DR: Black tea is good for health for a variety of reasons. Read below for more.
Tea is generally good for your health consuming black tea can result in healthier living provided it replaces any sugary drinks/soda in your diet. This will result in a reduction in the amount of sugar and calories in your daily intake which will result in a healthier body-mass index in the long term (depending on your age, build, health condition, etc.).
Green tea has been shown to activate your metabolism and increase your metabolic rate which results in faster burning of fat/calories per day. See this article for more: Green Tea Boosts Metabolism, Protects Against Disease [WebMD].
Black tea while also being very good for you has not been shown to have the same efficacy with regard to health as green tea and thus, I would recommend a dietary regime of both green tea and black tea for the purpose of “health”.
If you want to try a black tea for health benefits, try our famous Darjeeling black tea: The Empress of India | First Flush Muscatel Darjeeling Tea