I don't see why the different matter shouldn't be able to exist in our universe (unless it was anti-matter). How we would perceive this matter depends on whether and how it would interact with our own matter. For example, dark matter (if it does exist) doesn't interact with any of the four forces (electromagnetic, gravity, weak, strong), let alone light, making it a nightmare to detect. Provided their matter is capable of interacting with the electromagnetic force at least, then we should be able to perceive them. 

Isn't this a wee bit hypothetical?

What kind of other universe? What would be "other" about it?  If our kind of matter doesn't exist there, and theirs doesn't exist here, then in each case, why not? After all, without that being defined, how can we define the answer to the question? Do we even know why our kind of matter exists here, never mind there? Last I heard we were still failing to find the Higgs, right? And it has been suggested that the reason for the nature of our kind of matter has a good deal to do with how many dimensions we have. If the "other" "universe" has different dimensions in different roles, then how could it survive here? Could we survive in flatland? We aren't built to be silhouettes or shadows.

Does our kind of energy exist there? If so, then why? If you moved their kind of matter into our universe with its different parameters, then why should it not come unglued? And release what? Energy? Whose kind of energy?

If our kind of energy doesn't exist there, why should their matter release our kind of energy here, let alone exist here? If the chain of ifs were to become too tenuous for  too long, woudn't the question over-extend its own interest and fizzle out without energy?