The actual Minecraft Contained no plot or objective what so ever but let the players decide what to do in the incredibly nonlinear world. Episodic point and click games weren't my cup of tea, They felt more like a movie instead of a video game leaving little input from the player. Minecraft story mode gives you a character named "Jessie" and you have to answer choices/ decisions (while most of the time under a time limit) through the entire adventure, sometimes you be given quick time events, and being able to actually control the character(s) in the story. Granted there is replay value for choosing other decisions seeing what kinds of things will come up when you pick that card, but I find it really boring and not fun at all. The story is pretty much the main focus of the game (if it wasn't obvious enough) and it's somewhat interesting when you get into it, but that's all the game has got going for it, the story.
If anything I recommend the "actual" Minecraft because that's something you can have hours and hours of fun with since your given endless possibilities and creativity and isn't anything that can bore you in the virtual world. If you wish that Minecraft contains some sort of plot or objectives (unless if you or friends make your own adventure in the Minecraft world or mods on the PC) then I guess Minecraft story mode is your best option.