Most tea has caffeine. A cup of black tea has less than half the caffeine of a cup of coffee and a little less than a typical can of cola. A cup of green tea has a little more caffeine than a cup of decaffeinated coffee.
You might be referring to theanine, which is a natural amino acid. It does have an effect on the brain, but it's normally considered a positive effect of reduced stress and increased relaxation. I haven't heard of any negative effects of theanine.
Yes, tea is healthier than coffee. While most tea does have caffeine, the caffeine content is quite low unless you drink a lot of black tea. Green tea and white tea claim to have more health benefits due to their lower level of processing, lower levels of caffeine, and higher levels of antioxidants.
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