From a role playing perspective, the branching quests in Fallout New Vegas felt noticeably more weighty.
If I'm RPing a pro-NCR Courier Six, and I'm doing the Sharecropper quests (there where actually two seperate ones, tied into the area, if I recall correctly), then I want the Sharecropper farms to suceed. I don't want to battle my way into Caesar's tent and kill the bastard only for the NCR's Mojave operations to be crippled by a logistical oversight like farming.
And in one quest I had to make the choice to effectively damn one of the few surviving independent towns to ruin and killing a petulant anarchistic Follower, and risk ruining my relations with his faction I've worked with in Freeside to improve the state of things there, if I want to correct the water shortage problem. In universe, there is no way to no kill him and fix the NCR's water shortage. So, my courier made a choice to effectively cut off Westside from a major resource, most likely killing the town in the near future.
Secondly, in Vault 34, the source of the radiation problem in the Sharecropper farms water, I fight my way through ghouls and after navigating countless locked doors and password-locked rooms, I get to the reactor. At this point I'm greeted by a family of survivors from the vault, who want to get out. But to do that I need to open the ventalation shafts, effectively flooding Sharecropper farms with radiation, once again killing it's chances. But to support that farm, I need to turn off the reactor and seal the ventilation shafts, killing 4 innocent people. From a role playing perspective, no matter what I do I will be fundamentally screwing people over, and I'm forced to make an ultimatum, and I choose to seal the ventalatin shafts, saving the Sharecropper farms.
If both quests are completed in that order, that region of the Mojave will survive, and thrive. If even one branching choice is made, that NCR set up will disband, and it will damage the faction I'm championing in the Mojave. But to ensure that future I have to do very, very morally dubious things.
I apply the same argument to misc. sidequests all throughout Freeside, Camp Golf, Camp Forlorn Hope, etc. Each one of those sub regions has dialogue, or epilogue detailing the lasting effects of my choices. If you ignore those optional locations, during the Second Battle of Hoover Dam you can turn on the radio and learn how each one is effectively going to [censored], in the worst possible ways.
And I guess that's what I mean. Even if the effects of my actions aren't visually immidiate, the story informs me that my actions will have lasting impacts on the world as a whole. It tells me this, the dialogue is there. Unlike Bethesda's Fallout 4 I don't need to invent headcanon to justify my actions in the greater scheme of things.
Painting the wall in Diamond City, Helping Trevor, exposing the Mayor as a synth loyal to the Institute------none of these have lasting impact outside out the isolated bubbles the scripted events/quests take place. I've said it before and I'll say it again: the Minutemen story, which had the greatest potential to justify the onerous settlements ingame with a grand story, stops dead after The Castle. If I commit 100% to the Railroad and take pro-synth actions, or express pro-Railroad sentiments (like with that father and son in Bunker Hill), none of that has any lasting impact in the Commonwealth as a whole. Nothing I do matters outside of the side-quest bubble I'm completing.
I guess that's what I mean by depth, or meaningfully impacting the world. Yes, you have these grand scripted events, but when you get write down to it the world itself doesn't budge an inch the second you complete that final faction quests. Even those terrible radiant quests where I have to save a synth every 5 minutes carry no weight in the world itself.
For a game that is so ambitious to tackle McCarthy-esque speciesm and paranoia, it never felt like I was pushing the state of things one way or the other outside of the quests. There is no dialogue to reflect that, there's no passing comments to reflect that. Etc.
I hope that comparison makes sense.