There's no such thing as "any other science." There is science as developed and practiced by qualified researchers all over the world - including India - and it's all one and the same science, which is a set of protocols for rigorously checking the relevance of what you're seeing, and the huge body of useful human knowledge that these methods have brought forth. And then there's everything else, which encompasses "folk wisdom," quackery and outright fraud. If Ayurveda and its kin provided comprehensive documentation of rigorously controlled, published and peer-reviewed studies, it would be science; as it doesn't, it isn't.
What, exactly, are you talking about here? It'd be better if you could cite examples.
Does it have predictive (and thus real explanatory) power? Imagine a test (other similar tests can be imagined):
give some powder to a western chemist/biologist and an ayurvedic to examine its "elements". You are not allowed to feed it to any human or animal. Decide if it is poisonous! Who will be more successful?
Ayurveda knows nothing about modern chemisrty or biology (real elements, cells,...), its theory part is rubish (from the perspective of natural science not from social science perspective (history, philosophy...) of course).
You may trust its experimental results, but that is not science in itself just a tradition...