It is not the same type of caffeine as coffee.  Green teas contain two caffeine metabolites (caffeine-like substances): theophylline, which is stronger than caffeine, and theobromine, which is slightly weaker than caffeine.
Theobromine has a similar effect than caffeine, but about 10 times weaker. Theobromine has diuretic, stimulant and relaxing effects. Theobromine can lower the blood pressure because it can to dilate blood vessels. Theobromine has stimulant properties, similar to caffeine. Unlike caffeine theobromine does not affect the central nervous system. Theobromine can also relax bronchi muscles in the lungs. Theobromine can be used as cough medicine. Studies indicate that theobromine acts on the vagus nerve, which runs from the lungs to the brain.Theobromine is mainly found in cocoa beans (about 25 g/kg), and consequently in chocolate. Theobromine levels are highest in dark chocolates (about 10 g/kg). Milk chocolates contains about 2 to 5 g theobromine per kg. (1-5 g/kg). Theobromine is also present in tea and cola nuts.
http://en.wikipedia.org/wiki/Theophylline
I would not worrie about this at all so many great benifits to drinking green tea. I would still drink it if not for the caffiene gives me too much anxiety. My anxiety is too intense. I miss it terribly and it helped my bladder pain a lot.