When comparing pygame vs Flixel, the Slant community recommends pygame for most people. In the question“What are the best 2D game engines?” pygame is ranked 16th while Flixel is ranked 20th. The most important reason people chose pygame is:
Pygame uses Python as its scripting language. Python is widely considered one of the easiest languages to grasp even for beginners.
Specs
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Pros

Pro Easy Python syntax
Pygame uses Python as its scripting language. Python is widely considered one of the easiest languages to grasp even for beginners.
Pro Very easy to understand
The API is very straightforward.
Pro Good canvas system
Pygame has a drawing system that allows the user to create and draw on an unlimited number of canvases.
Pro Many ports available
Ports are available for Objective C, C# (XNA), HaXe and Monkey X.
Pro Built-in pathfinding and following
Pathfinding just means figuring out how to (or if you can) get from A to B. FlxTilemap has a function FlxTilemap.findPath() which returns a FlxPath object, which is just a collection of "nodes", or FlxPoint objects.
Pro Camera system for split screen
Create effects like "split screen" views, or "picture in picture" style displays, or even mini-maps with FlxCamera. Each camera is an independent display object, with its own zoom, color tint, rotation, and scaling values.
Pro Record and play back replays
Replays are essentially a list of what keyboard keys were pressed, and what mouse inputs were given, during a specific time frame. Because Flixel is largely deterministic, you can use that information to recreate a gameplay session that someone else recorded, as long as you have the same SWF.
Pro Basic features provide a solid foundation
- Display thousands of moving objects
- Basic collisions between objects
- Group objects together for simplicity
- Easily generate and emit particles
- Create game levels using tilemaps
- Text display, save games, scrolling
- Mouse & keyboard input
- Math & color utilities
Pro Flixel Power Tools extend the functionality
Flixel Power Tools provide a set of classes and APIs that provide more functionality.
Pro Used to create Canabalt, game that started endless runner genre
Cons

Con Deathly slow
Con Nonexistent community
No good forums, wiki, or other ways to reach other Pygame developers.
Con Very basic
Pretty much just a wrapper for SDL.
Con Pygame is a multimedia framework, not a game engine
Physics, AI and networking are not supported.
Con Messy documentation
The docs are messy, and some basic functions are infuriating to work out. There's even some places in the documentation where it's clearly wrong about how a method is called/what the arguments really do.
Con Outdated
Pygame uses a really old version of SDL and is missing some of the features developed for SDL2.
Con Hasn't been updated in years
Hasn't been updated in years.
Con It is now obsolete
With Adobe Flash dead, Flixel is now unworkable.
Con Development has stopped
Seems like development for Flixel has stopped. The last commit on all of the branches of it's Github repository are from 2011.
Con Poor performance on mobile
