This is a topic I've researched a fair amount.
I haven't found any direct studies comparing the health effects of green tea to black tea, or other types of tea. I have read some studies that compare the antioxidant activity of various types of tea, but these studies are of questionable methodology, and their conclusions are mixed anyway. Although green tea is often found to have higher antioxidant activity by certain measures, than black, this doesn't mean it's healthier--studies of the mechanisms by which tea influences health have questioned the idea that the antioxidant activity is responsible for the health benefits.
I think right now, we can just say "we don't know", but also that it's been established in general that tea, regardless of type, is healthy.
One thing I will say, the chemical composition of tea varies hugely between different grades and quality levels of tea--caffeine content, antioxidant content, all sort of other things. So...the quality of tea may be important. This doesn't necessarily mean that higher-quality tea is healthier, although I have an intuition that this may be the case (keep in mind higher-grade teas are also often higher in caffeine though).
It's complex...and in the end tea is just a drink. The health benefits of tea are always going to be small, compared to, say, the health benefits of regular exercise.