Theophylline is an alkaloid derived from Tea which acts as a mild bronchodilator.
In brewed tea, trace amounts of theophylline is present; only around 1 mg/L which is significantly less than a therapeutic dose. Tea has classically been used to treat mild asthma and bronchitis although other potent anti-asthma medications are available with more therapeutic benefit, tea may be beneficial for mild respiratory problems and is safe, even for children. But tea should not be used as a medication for Asthma.
The difference in the quantity of theophylline between green/black tea is insignificant.