Moai SDK vs HaxePunk

Because it uses Lua + C++.

You can use your own custom shaders and extend the language with C++. MOAI doesn't give you everything, instead it gives you the tools you need to develop any game you want.

So it is extendable with C++

Uses a limited subset of Lua

Moai SDK is used by popular developers including Double Fine for their mobile game, Middle Manager of Justice, and for their Kickstarter hit, Broken Age(formerly, Double Fine Adventure.) It was also used to create the popular mobile game Bubble Ball 2.
This proves that this engine can be used to make fully-featured and fun games.

Has options for development like Hanappe and Rapanui, providing a different way to interact with the engine.

The Moai SDK Forum is active and users will go to great extents to answer queries, post code snippets, beta test, and even purchase and give feedback on each others' games.

Although the Moai SDK is very advanced and uses complicated features, the documentation wiki thoroughly and clearly explains how to use these features, such as the Moai Cloud(a service that provides web services for your game), and multiple ways to build from source.

Useful for mobile games and soon consoles (OpenFL has a console port in the works).

HaxePunk uses OpenFL which means you can compile to just about every device. A lot of the rendering code has been optimized so if you use HaxePunk’s graphic classes you are pretty much ready to deploy on any target.

A generic Entity system that only uses what you “attach” to it. If you need collision masks they are available but if an entity doesn’t need to collide with anything then simply don’t add a mask. Same goes for graphics.

This comes with blazing fast compile times, proper static typing, multiple output targets, and a powerful macro system.

HaxePunk has added several collision masks beyond what FlashPunk had including a grid with slope values, circles, and polygons. This is in addition to FlashPunk’s tile grid and hitbox.

Tweens are available just like they are in FlashPunk. If you need to interpolate values for sounds, movement, etc… it’s probably already available as a tween. There is also a VarTween that lets you interpolate any value you want.