Hi,
tl;dr It’s current, simpler to use, and more full featured. 
Some of the advantages of the new plugin are:
- Rebuilt code base from the ground up (mod_parse is aging in Internet years).
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Full access to the Parse API, with a framework to add any new functionality easily.
- A more ‘query’ like syntax to make it easier to work with the API, including full support for all query operators.
- It’s a Corona Plugin (not a stand-alone module) so updates and distribution are easier to maintain.
- Completely documented, with lots of conversion examples from Parse JSON to Lua.
- Lots of under the hood improvements.
One of the main sticking points most reported with mod_parse is dealing with complicated queries, and how to format those properly. The aim of this plugin is to remove that friction as much as possible with a clearer and simpler syntax, and more in-depth documentation addressing that process.
In addition, the code base will be easier to keep up to date, allowing me to add new Parse functionality as it’s released (as long as it’s included in the REST API of course).
If mod_parse is working for you, you can keep on using it for the simpler use cases, but if you want to get more control over your queries, and access to Parse functionality in general, the plugin will be the way to go. Additionally, mod_parse will not recieve any more updates (except bug fixes) once the plugin releases.
Hope that helps. Thanks for the kind words.
Cheers.