Objective C, a derivation of C (that uses lots of [] and looks real st00pid) is the official language Apple supports / uses to develop Mac and iOS software… So, you would use something in your app to interface to their obj c code (or develop iOS libraries like the add ons to corona for advertising, gamecenter, etc, using obj c)
And on the Android side, Java is the official language. To make a gamecenter library corona (or others) could use for android, you’d need to build the android gamecenter code with java (also a descendent of C).
Objective C can’t do much more than c that I know of. They changed the syntax though so that it would compile and execute a little faster (and the code is terribly unreadable imho). But it runs fast, gotta give it that.
Java is kind of the opposite. It reads more like BASIC, and doesn’t ever really compile (read as slow, comparatively, to C). I probably should mention all of the security issues of java… It’s got so many little features built into it, and runs on so many platforms that hackers have had a field day finding ways to exploit the vulnerabilities.
Lua is somewhere in the middle. It doesn’t compile like obj-c, but is a much more streamlined language than java.
Finally, lua seems just fine for all types of applications (except database I think, but you can get libraries to help out there – there’s a mysql library added to corona for example). Perhaps it wouldn’t be the greatest at hard core computations (like cracking primes) where ultimate speed counts. For apps like that, a compiled language like C would provide better speed.
But for moving sprites, popping bubbles, or throwing birds around - Lua works just great.
Speaking of libraries - that’s probably one of the more important things to consider before approaching an application. Choosing the right tool. If you’re making a twitch game, choose a tool that would make it easier (like corona). If you’re making a program to calculate the positions of every star in our galaxy 200 years from now… Maybe not so much… So look around at the libraries/features any particular platform you’re considering has. If it’s not in there, you’re going to have to either modify your design, find a library that provides it, or build the support yourself.