jMonkey3 vs Solar 2D (formerly Corona SDK)

Java is a well-optimized just-in-time compiled language. It's faster than languages without an effective native-code compiler such as Python or Ruby, similar in speed to other just-in-time compiled languages such as C#, while slightly slower than compiled languages such as C or C++ (with some low-level and numeric benchmarks being similar to C++).

Java also has a wide variety of high-class IDEs available.

Code can be ported to mobile (iOS is in the works) and other Android supported devices with minor changes to the code (just change some implementations that vary on the platform such as inputs and user interface). It can even run on certain Raspberry Pi devices.

jMonkey is completely free, meaning it's possible to develop and release a game with no fees or royalties. Because it is open-source, jMonkey has plenty of people fixing bugs and, adding to the engine as well as creating a variety of plugins that can be used in the engine.

Unlike some engines, jMonkey doesn't force its own IDE. You can use its Netbeans-based IDE, but you can also set up a project to work in another IDE such as Eclipse. You can still use the special tools from jMonkey's IDE in such projects.

Because jMonkey is implemented in Java, the same language its apps are typically developed in, developers will have an easier time modifying the engine to their needs.

jMonkey3 handles input from computers and mobile devices. It handles networking, physics, rendering, terrain, and cinematics.

Engine is modifiable.

The user is not compelled to use any programming architecture nor standard in order to make a project working. JME allows the freedom to use what is best for a game.

Modifying shaders can be done either via a visual tool called Shader Nodes or via GLSL that allow you to make your own shaders without the engine getting in the way or having to hack around to do so.

Corona SDK is completely free. That includes pro-tier plugins.

Corona SDK ships with Corona Simulator, which runs your game/app directly on your PC/Mac and updates every time you make changes.
It provides immediate feedback to your actions, you can see your changes right on the screen, without necessity to make build to device. Getting instant feedback really boosts tenfold prototyping and development speed.

It's easy to create a game that looks good on many different sized mobile devices.

With the live build feature, once you have created a build and installed on a device, you get lightning fast turnaround times because any change on the code or data is updated to the devices running the game (within the local WiFi) immediately. So changes can be tested on the real hardware within a very few seconds.
What's even more impressive, this even works flawless with multiple devices running the game. You have to use it to learn how good of a feature this is while development and even more, while doing QA. Imagine fixing bugs and everyone of your QA team/friends/whoever helps to get your game done, has all changes on his device without doing anything but waiting 5 seconds - outstanding.

Uses the great and easy-to-learn Lua programming language.

It's very quick to get things up and running with Corona SDK. The API is extensive and while it's not 100% feature-complete with the iOS API, it's close enough that you could create tons of games and never run into a roadblock.

The API docs can be found here.

Corona does not throw photoshop-like madness full of buttons editor. You can go as fast as you want, learning and building game from ground up. Eventually, you'll learn how much corona is doing for you. But to start you don't have to master complex editor software. It's a great tool to learn to start game development if you want to learn how to program and make games. Your experience will be 100% transferable to any other Pro game engine.

Corona works on OS X, Windows and Android (including Kindle Fire & Nook).

Since Corona SDK became Solar2D, it's completely free, as only some third-party plugins are paid.

Since Corona SDK became Solar2D, it's completely open source under MIT license.