There are differences.
- Loaders Modernized is powered the electric grid. AAI consumes fluid (default - lubricant) as "fuel".
- Each have a setting option to turn off their "power" requirement.
- Their recipes are different.
- The aesthetics are different - although Loaders Modernized can use the AAI graphics.
There may be some other minor differences in features exposed and implementation. Mostly it is preference and play style that drive the choice.
Miniloaders was a Mod implementation in Factorio 1.1 that was very different in capability and implementation than AAI Loaders at the time. It was based on hidden inserters so that it could interact with rail cars, interact with circuits, consume power, etc... AAI Loaders could not do those things in Factorio 1.1. In the world of Factorio 2.0 the in-game loader entity was improved considerably. Mini-loaders were not compatible with Factorio 2.0 as-is and the developer of was inactive so, I created a path forward for those players. Loaders Modernized's implementation uses the improved in-game entity. AAI Loaders also saw the improvements because it was always based on the in-game entity. There is also now Miniloader (Redux) (also a fine mod) which created a new, 2.0 implementation using hidden inserters like the 1.1 Miniloader mod. It brings a few interesting quirks to the party that is of interest to some players.
At the end of the day, all three provide a similar function with a few variations in implementation. It will come down to personal choice of which combination of features you're interested in.
