Preface
Everyone you know has a smart mobile device of some kind. You probably own several! The general idea of having utility applications on a phone is not new, and even cell phone and PDA games have existed for years, but the way that the iPhone used touch instead of a stylus or keyboard, and gestures to reduce the number of steps to do something, was a game changer.
The iPhone was released in June 2007, and Android OS in September 2008. If you wanted to create something that worked on both platforms you had to learn two development environments and languages; Objective-C for iPhone, and Java for Android.
In the desktop world there are several development tools that do allow you to publish to both Mac and Windows, as well as Linux in the case of LiveCode. The most successful of these tools are Adobe Director, Adobe Flash, Unity, and LiveCode. Publishing to iOS is being worked on for Director, which will mean that all four tools are also suitable for developing for mobile.
Those tools have different strengths. In some cases the strengths relate to the nature of the applications you can make, and in other cases it relates to how accessible the tool is to people who are not hardcore programmers. If you want to make a high quality 3D game, Unity would be the best choice, with Director and then Flash as other choices. If you need a lot of character animations, then Flash would be the best choice, with Director being a good alternate.
If the important thing is how approachable the tool is, then LiveCode wins easily. It's also just as valid a choice for making the majority of apps you might wish to. In fact, for apps that are a set of single screens, as would be the case for most utility apps, as well as for board and puzzle games, LiveCode is better suited than the other tools. It also has better access to native interface elements; with the other tools you usually have to create graphics that resemble the look of native iOS and Android controls, instead of accessing the real thing.
With its easy to use English-like programming language, and the "stack of cards" metaphor, LiveCode lets you concentrate more on creating the app you want to make, and less on the technicalities of the development environment.