-Regular coffee (16-20 oz./daily), High quality coffee of course.
-Decaf coffee (16-20 oz./daily), High quality coffee of course.
-Green tea (4-8 cups/daily)
-White tea (4-8 cups/daily)
-No caffeine
It seems there are two primary factors governing the health effects of these drinks--caffeine and antioxidants (or other bioactive compounds).
Research has shown independent and synergistic effects of each of these compounds in moderation, with potential negative health effects in excess. This means that drinking regular coffee/tea over decaf could be more beneficial for you, but if for whatever reason you don't want the caffeine then you'll still get some benefit from the bioactive compounds left in the decaf. Conversely you could use just caffeine and get some benefits separate from the bioactive coupounds in these beverages.
The research also seems to suggest that too much caffeine, or a high sensitivity to caffeine (slow metabolizers), can have a negative cardiovascular effect that at some point will overwhelm the benefits of the other bioactive components of these beverages. If you are a slow caffeine metabolizer then your caffeinated beverage threshold is much lower than a fast caffeine metabolizer, and as such you'll get less overall benefit because your lower beverage consumption will contribute less antioxidants/bioactives.
Coffee and tea also have their own bioactives profiles. While green tea (and white is right up there) seems to have "more" antioxidant capacity (probably depends on how you measure it) and more robust epidemiological evidence to its benefit, it's very difficult to directly compare the two. Though tea does have theophylline while coffee doesn't. It's like asking if you should eat broccoli or blueberries. Both are healthy, and you're probably better consuming some of both.
The last thing that I'd think of is potential downsides. Depending on the brand, growing conditions, etc., green tea can be quite high in fluoride, aluminum, and similar, and coffee can be high is pesticides and other chemicals. Brewing methods could alter the exposure to some of these. Brewing method is also important for coffee regarding fiber and other soluble factors, as these seem to have an effect on plasma lipids and cancer risk.
I used to drink at least a pot of coffee before 7 in the morning. I stopped that crap now and switched to green tea and black tea instead. It did wonders in helping me with the cortisol level.
This is a great example of why moderation is important. Drinking less coffee could have the same effect as switching to the lower-caffeine teas.