short version: The goal of Tedster's Modjam is to be a spiritual successor to Kiruka's Modjam, while the goal of Minimalistic Modjam is to be a rework, with the vision of only applying minimal modifications to the mods in the modjam.

longer version:
- no code changes, so no things like new corpses and new projects (besides the ones added by the mods themselves), but also lower chances of conflicts and bugs with mods outside the ones in the modjam and more customizable for regular players
- avoid overhead of choices/items, so no gene mods, and no immolator (the weapon is cool, but technical basically already has it, but with perks that support it and without extra weapon mods)
- different approach to psi soldiers (in this modjam it is similar to xcom 1)
- allow extract corpses, and thus change the economy balance in the blackmarket accordindly, so the corpses sell cheaper (the reason is that I consider that being blocked by the RNG is way more frustrating than challenging)
- different set of supported enemies
- different set of supported classes
- add new random perks to the xcom pool (or just different... don't know if tedster added it too)
- many differences on fine-tunings and game balance choices (for example, there are things they nerfed/buffed that I approached differently, and vice-versa. For example, I applied a stronger nerf to flame vipers burning skill in the early game and avoided adding enemies with burning skills to the early game, but I applied a ligher nerf overall to the new requiem enemies stats. Regarding items, I nerfed more Infiltration Protocol, but allowed Winter Fangs, for example)
- overall more mods (since I tested all of them, I didn't see why not disponibilize them as optional mods)
- more AP points for soldiers
- overall both the soldier and the enemies are a bit stronger than the original LWOTC


(be aware that both Minimalistic Modjam and Tedster modjam are based on Kiruka's modjam, so there are also many similarities)