Solar 2D (formerly Corona SDK) vs CryEngine

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.

CryEngine has some C#template and also C# based system to write your function/ideas in to your game.

CryEngine 5.4 now supports DX12 and Vulkan

Cry Engine has volumetric fog rendering which allows for realistic cloud shadows that actually render shadows onto the fog itself. Combined with their time of day system, it's possible to create incredibly realistic weather effects. On top of this, color grading allows user to post process pallets allowing them to change the color tone for different type weather, such as using a deep dark blue for rain.

It can shoot, walk on patrol points, can see the player and so on.

Cryengine (starting on Cryengine V) has Virtual Reality support. Developers can create games with VR support for multiple platforms: PlayStation VR, Oculus Rift and HTC Vive.

Cry Engine has realistic water effects that even simulate ocean physics. Features such as waves that respond to global wind, and dynamic water volume tessellation allow for some of the most realistic water effects available to a game developer. The engine also takes into account LOD (level of detail) on water geometry to allow it to stay performant for water at a distance.

Where Cry Engine really shines is with rendering scenes of nature. The Crysis games feature incredibly detailed vegetation and weather effects and it's the Cry Engine that enables that. The engine has many features to create a cohesive realistic looking world. Dynamic water effects allow users to have beautiful oceans, fog and cloud effects allow for realistic weather, and a plethora of lighting effects optimized for natural looking scenes make Cry Engine one of the best engines for creating vast beautiful landscapes.

By having all these features built together from the ground up, Cry Engine is capable of doing more complex effects more efficiently, than other engines that didn't have these effects planned from their inception.

Supports miltiple platforms including: Xbox One, Xbox 360, PS3, PS4, Wii U, PC, iOS, and Android.

Flow graphs resemble flowcharts where each box represents a function or value, with connections between them representing program flow. This provides a better at-a-glance indication of game logic than a simple list of events, and makes complex behaviors easier to accomplish.

Crytek has launched a dedicated Q&A forum for everything Cryengine related. It's called Cryengine Answers and it's a community dedicated to sharing and answering any question related to Cryengine.

The Cryengine marketplace is an online marketplace which enables developers to access and use individual assets from thousands of materials, sounds and 3D objects created by the community. Even Crytek's own library assets are available there.

Cryengine has an optimized volumetric cloud system for Virtual Reality to give clouds full 3D spatial rendering. This ensures a high rendering quality with a minimal performance hit.

Simply by looking at the RC log when exporting can greatly improve your work. Cryengine doesn't handhold you constantly and helps greatly with avoiding bad practices in asset creation.