I'm pretty sure that's exactly backward, black tea has the most caffeine, then green, then white. That's with all thinkgs being equal (ie. all leaves, or the same mix of buds and leaves). Also, green tea in particular (I'm not sure about white) has another compound in it called theanine that somehow counteracts the stimulant aspect of caffeine, so even though there's some caffeine in green tea it doesn't cause stimulation. Basically, the longer the tea is oxidized (fermented), the more caffeine there is.
Also, by weight there is more caffeine in tea than in coffee, but you use a lot more coffee when you make a cup than you do tea. So that is why coffee is higher in caffeine when you drink it.
As Kevink says, there are a number of healthy compounds in teas (antioxidants in particular). One cup of green tea provides 10-40 mg of polyphenols and has antioxidant effects greater than a serving of broccoli, spinach, carrots, or strawberries. White tea has even more, but I'm not sure how much.