I've only played New Vegas, so perhaps I'm missing something important from the previous games that could have swayed me away from the following opinion. (But I generally don't play older games if I enter a series on a sequel, because the quality lowering is distracting.)
I think I would like the opportunity to go through time a bit. Not time travel (necessarily), but after you do something huge, I would like the chance to fast-forward several years and see what good or bad your decisions had done. New Vegas ended sort of abruptly for me, after helping Yes Man and talking my way out of both final bosses (yay Speech 100). I would have much rather liked it to have its "ending", but then let me play the second half of the game in the new world I was responsible for creating. I want to know more than the few sentences the epilogue gave me to go on -- I want to explore my independent New Vegas, I want to see what's left of the NCR and Legion, and I want to make more decisions from my new position of power. Of course, I don't expect them to do New Vegas Extended Edition, so replace those group and location names with the new ones in Fallout 4, but same concept.
I think I would like the opportunity to go through time a bit. Not time travel (necessarily), but after you do something huge, I would like the chance to fast-forward several years and see what good or bad your decisions had done. New Vegas ended sort of abruptly for me, after helping Yes Man and talking my way out of both final bosses (yay Speech 100). I would have much rather liked it to have its "ending", but then let me play the second half of the game in the new world I was responsible for creating. I want to know more than the few sentences the epilogue gave me to go on -- I want to explore my independent New Vegas, I want to see what's left of the NCR and Legion, and I want to make more decisions from my new position of power. Of course, I don't expect them to do New Vegas Extended Edition, so replace those group and location names with the new ones in Fallout 4, but same concept.