Honestly speaking, I haven’t played Minecraft, so I can not really compare the two.
I started playing Minetest in its early days, more than 10 years ago. (I registered minetest.net domain for the first time, and when community and forum started to grow there, I handed it over to the main developer)
There were some funny stories from those days.
For example, the first introduction of monsters shooting fireballs was an ecological apocalypse:
monsters were spawning randomly in the dark corners, and then started to shoot fireballs randomly (but only horizontally), and fireball explosion cleared walls.
So you started to play a game, exploring and building stuff on the surface, green grass, sun and clear sky… And at the same time, underground the growing monster horde was clearing out everything on its way, turning it into enormous flat underground parking lot filled with monsters, waiting for you to come down for mining.
They patched it later, but definitely made me thinking about how you can not just introduce a new species of monsters in your game world, and have to think about balance and food chain.
Nowadays, the main feature of minetest, according to devs, is that it is not just a sandbox game, it is an engine, on top of which you can build additional mechanics.
And there is a library for them: Games - ContentDB
For example, there is “minecraft clone” MineClone 2 - ContentDB
or there is also a box puzzle: Box World 3D - ContentDB
And of course there are mods. I should probably try this one Techage Modpack - ContentDB