There's usually a few downsides to developing with any kind of cross-platform solution.
1. You won't be writing apps in their native languages (ie. objective-c for iOS and java for Android). Instead, with Corona, you'll be writing your apps in Lua, which is a scripting language.
2. A lot of times not writing apps natively can negatively impact the performance of an app. I can't speak for the Corona SDK directly, but using 1st-party tools and languages properly should always yield the best app fluidity, responsiveness, and performance.
3. You will be directly limited by the Corona SDK. What this means is, when you are developing your apps, you won't have the luxury of being able to use the latest and greatest technologies. You will have to wait for Corona to add those specific features into their own library, before you'll be able to gain any benefit from them.