Solar 2D (formerly Corona SDK) vs O3DE (previously Lumberyard)

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.

As a proof of how much Amazon is committed to the project.

Advenced stereoscopic reprojection to save rendering time.

Sculpting and painting tools for terrain and instanced details.
Procedural generation of terrain.

Built-in support for roads and rivers to ease the design of rich game environments.

Full source code for Engine Editor and every tool.

Thanks to built-in terrain, time of day, ocean and volumetric fog systems. There is also a gfx pack with various environmental meshes, cloud, particles, materials and skyboxes.

Multiple entity contexts, reflection, serialization, replication, script binding, event bus (EBus) messaging, fully cascading prefabs (slices).
Every reflected property can be fully exposed in the editor with a customizable gui control and can be animated in the built in animation tools.

Online oriented plugins composed by both client, server and administration components to easily add various online capabilities without further work (es leaderboards, login, message of the day, downloadable contents).
Since version 1.7 they has been released at a steady rate.

Very advanced 3D prototyping tool with many modeling features and UV mapping support available. If you want you can build any kind of fully textured static mesh without relying on external tools.

Realistic looking lighting bounces.
It doesn't require long offline precomputation times like other static and dynamic GI solutions based on lightmaps or other similar techniques.

Other than common aws functionality it supports game specific Game Lift for autoscaling game servers.

Modular workflow and flexible cascaded propagation of changes.

To easy add and remove modular functionalities to a project and easy share them.
Modules are called Gems and can contain code and/or assets.

Tessellation and Displacement.
Various Parallax Mapping techniques(POM siluette).
Translucency and Sub surface scattering.
Detail Mapping.
Material Blending.
Emission.
Advanced uv transformation and animation.

Global environmental volumetric fog and/or hand placed custom shaped volumes with featuring full lighting and shadows.

Amazon made available a selection of triple A quality scenes filled with high quality assets.

Implements the most recent technique available (published in 2017) from Anton Kaplanyan.

You can modify shaders while testing the game.

Shader files are modular and annotated to setup the material editing gui and filter out mutually exclusive options. All shader permutation are compiled almost instantly from the asset processor and cached for later use.

You can create games that react to keywords entered in a designated Twitch channel and let streamers to invite targeted viewers into their game sessions on demand with ease.

It is still possible to use the non LTX version with few changes.

Built-in Lua editor with remote debugger to debug Lua scripts running in any device.

Optimized versions of assets can be streamed live to any device connected over the network.
This makes possible to implement asset types that hot reloads reducing drastically the time to test new content and little changes on device.

Multiple grain of control over any kind of engine setting and various kind of Lod systems. Settings can be grouped and applied in batch.

Perforce also comes with a free version for a limited number of team members.

Has skin shaders with subsurface scattering and weighted wrinkle maps, eye shaders with refraction parallax, hair with anysotropic specular reflections, etc.

A must for problematic things like hair , vegetation and scenes with complex solid transparent objects(es glass of water with ice cubes).

Special iteration of Temporal AA to battle the ghosting issue omnipresent in engines using other Temporal AA techniques.

It now works for both static models and animations and support advanced setups(es lods and physics).

Updated renderer pipeline to leverage the full spectrum of precision, luminosity and image processing features of the latest HDR tv.

Animation Spline editor supporting huge range of keyframing and tangent editing tools.

The UI uses the entity component system so it's fully modular and easily expandable. The UI is easily skinnable and supports border scaling images (scale 9). Powerful layouting system supporting multiple screen resolutions. Being based on the entity system every property can be fully animated.

It is elegantly managed in a separate entity context so it doesn't get messed up with other kind of entities and their components like in other engines, but it's fully decoupled communicating with entities in other context on specific event buses.

See here.