If you haven't played and beaten Fallout 1, 2, and 3 then this will contain spoilers
In Fallout 3 you emerge from Vault 101 searching for your dad, James. Along the way you meet Three Dog who is running a radio brodcast program with a few members of the Brotherhood of Steel as security. The Brotherhood of Steel is in D.C. searching for the pre-war technology left there, or they were. Now Elder Lyons became attached to the people of the Capital Wastleland and decided to stay there and help them with their Supermutants, raider, slaver, and Talon Company problems. Those who opposed became the Outcasts, who stuck with the original goal. Three Dog tells you how James went to Rivet City and then you eventually end up in Vault 112. After escaping the Tranquility Lane simulator and having a rather dull meeting with your dad you head back to Rivet City and then to the Jefferson Memorial. But the Encalve arrives nad your dad kills himslef to buy you and the other scientists time to escape. Once you do so you end up at the Citidale where Elder Lyons lets you in and sends you out to find a GECK. Once you retrieve that you are captured by the Enclave and escape. Once you get back to the Citidale you join Lyons' Pride and Liberty Prime in taking the Purifier back from the Enclave. Once you get inside and confront Colonel Autumn you either sacrifice yourself or Sarah Lyons in typing in the code for the Purifier... or you let it explode.
In Fallout 1 you emerge from Vault 13 into Shady Sands trying to find a water chip, after you do so you must fight the Master and his army of Supermutants. Once you defeat him you return with the water chip and then banished from the Vault, either just walking away or shooting the Overseer in the face. (Sorry it's so short, never played it)
In Fallout 2 you leave the Vault Dwellers settlement as his grandson and must find a GECK. After which the people of Arroyo and the people of Vault 13 are captured by the Enclave and you must sneak onto their oil rig, free the people, fight the president, and Frank Horrigan. After that you destroy the Oil Rig. (Again, I've never played it)
I know it's mainly due to me never playing the old games, but do you see the difference of the stories? If somebody who's played the first two Fallouts can do those descriptions better (I'm 99.9999999999% sure they can) then post below.
But I don't get the Original Players saying that Fallout 3 had a cut and paste story of the first two, when I first played it I found the story two be very deep... And please no mentioning New Vegas because in my mind New Vegas is almost as bad as the Burned Game, in my mind.
Edit: Sorry for the crazy long underlining...