You seem to be confusing federation and confederation. It is to be expected that the individual divisions of a federation are only partially sovereign. That’s why your question is too vague. The EU is a supranational union of sovereign states and the individual multi-party systems are too different to be clustered as one multi-party system in comparison to India.

That being said, even the individual multi-party systems in India are different from each other. While they belong together and do not differ structurally, culturally and historically they have their differences and there are different norms and problems. E.g. you have the absurd influence of cinema dynasties in a few states, and then in a few other states there is rather a stronger religious influence.