In the old days coffee had caffeine while green tea was said to have thiene, a similar but different compound. In more recent decades the science has proven this to be inaccurate. Camelia sinensis produces the exact compound, caffeine, as coffee, yerba mate, and other caffeinated plants. The difference in the feeling between coffee and green tea comes from the different alkaloid profile of each organism. In particular, C. sinensis produces a compound called L-theonine, an amino acid, which promotes calmness and relaxation while simultaneously slowing the absorption of caffeine into the blood. This creates a broad peak of caffeine levels in the blood versus the sharper peak provided by coffee.
So if your goal is sustained, not jittery energy then small doses of green tea is the way. If you need a burst of energy quickly then coffee may be preferable.