What will be the differences in sound when I Plug my headphones directly into the mooer vs when I run the mooer through an amp and then connect the headphones to the amp ? I'm just curious because I've been trying to buy a decent guitar setup for myself and I only have the option to either buy an amp or an fx processor in around 100$-150$ price range.
The GE100 is capable of amp modeling, i. e. emulating the behavior of a certain amp.
This may sound a bit or a lot different from what the actual amp sounds like, because modeling is not perfect. I do not know this specific FX pedal very well but you can get an impression of how good it sounds based on customer reviews and sound samples (Thomann should have some of those on their website).
TBH if you're unsure about if this is the right gear for you, stop asking questions here and go to a store where you can test-drive it (or have an employee demo it).