Lots of things I have read have stated that the Green cabs are essentially run by organized crime syndicates and you are asking to get held up if you are a tourist. There was a Wall Street Journal article on crime agaisnt tourists in mexico about a year or so ago, I guess. My father organized a trip for us last year and he also ran across several articles in travel magazines, etc about the green cabs.
As for other cabs, I don't know. We never traveled in any. But in Mexico City, the subway will get you most anywhere you need to go and tour buses will take you to any of the surrounding areas like Teotihuacan (definitely worth the trip. Take a full day and go there. A must see. But read up on it first. it's bewildering if you don't know what you're looking at, and there's a LOT to look at)
Tom
Tom