Seeing as I have only touched three of the main fallout games(F3, FNV, F4) and I felt the three I have seen have certain merits to each of them to give a feel fo the setting.
F2-The scene I remember is I think a vault opening with a family fo 4, one of them waving while a row of machine guns begin to spin up and gun them down with I think Enclave troops power armor soldiers being the ones.
F3-I started the game and as it slowly pans out and the somewhat eerie sing begins to echo as it pans out in the ruins of the Wasteland and an a perrson in Poeer Armor(I assume BoS) is looking in the direction of the music from a bus, as if he noticed the radio suddenly jerked to life and turning his/her attention to the radio surviving. Gievs a feel of "this is not Washing DC, this is the Capital Wasteland now.
FNV-For me with New Vegas didn't strike me as apocalyptic in the cinematic, but mroe of almost a prologue showing the parties and central place of note of the whole game. I We see the NCR drunk soldiers on on l4ave getting drunk, and securitrons moving about in the stri0, then the iconic Desert Ranger or NCR ranger shooting a Fiend from a distance, then further Legion movements near the strip. And then to Benning and the Khans. It felt like a "these are the major ppayers here. NCR, Mr. House, and Legion.
Fallout 4-Had a different take of with, real people, CGI and cinematic animations. Nate explaining the world and the current events before the events of the bombs dropped. It felt like a backstory of him when I played the game.