Green Tea has a different profile than Black Tea because less of the actives oxidize prior to harvesting (think green olives vs. black olives--green are picked less "ripe")
I don't know the chemical name offhand, but there are constiuients in Green Tea that offer all kinds of health benefits. I wouldn't say they "enhance" the effects of caffeine, rather work well in combination working on different things.
Green Tea is lower in caffeine that black tea, and almost all tea has less caffeine than coffee. But yes, drinking coffee and green tea will wake you up, certainly. I don't know about your "stimulates fatty acids" theory. That sounds like marketing lingo to me.
I personally believe you're better off just drinking green tea than taking extracts, b/c the synergstic effect of the substances balanced in their natural form has been keeping Asians healthy for centuries.
What would I do? A good ECA stack and drink green tea. If your moderately to highly active and you do these things, there is no way you won't lose a lot of bodyfat over a two-month cycle.