When comparing Ludum Dare vs Game A Week, the Slant community recommends Ludum Dare for most people. In the question“What are the best recurring game jams?” Ludum Dare is ranked 1st while Game A Week is ranked 7th. The most important reason people chose Ludum Dare is:
Ludum Dare has been running since 2002, with tens of thousands of entrants at every level of proficiency. As an industry-wide event, participation carries a sense of being part of something, and there's no shortage of interest or discussion online.
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Pros

Pro Long history and strong community
Ludum Dare has been running since 2002, with tens of thousands of entrants at every level of proficiency. As an industry-wide event, participation carries a sense of being part of something, and there's no shortage of interest or discussion online.

Pro Most popular game jam of all them
Pro Other people actually play your game
Pro A lot of mini jams
The main Ludum Dare event happens once in a year, but throughout the year, a lot of Mini LDs are held. Since I don't expect any great results at the main LD, which has countless participants including pros, I only do mini LDs. That's a lot of fun, because the community is large and people actually play your game in the events.

Pro Theme Voting == FUN
The fact that everybody gets to VOTE for an entire week to generate a shortlist and final theme which is announced in real-time to great fanfare is half the fun. It draws you in, gives you ideas beforehand, and generates a conversation online in the days leading up to each wonderful #LD48.
It is like a drum roll that gets you excited.
Pro Chance to see developers writing code
Multiple developer have set up streams allowing people to follow development process in real time. There's a public directory on Twitch with Ludum Dare streams.
Pro Flexible Schedule
You don't have to work on your game on any particular day(s), therefore you can work when it fits your schedule best.
Pro Informal Rules
Game A Week is more of practice than a contest, therefor you can apply rules to yourself that enhance your experience and creativity.
Pro Short Time Horizon
Having a quick deadline helps focus your effort and also keep your scope in check.
Cons

Con Theme can be too specific
The themes can be too specific, which can limit the creative game ideas.

Con The company of giants can be daunting
With regular entries from industry celebrities, a beginner has no reason to expect much attention, much less placement in the competition.
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