When I think about depth, I think about things like: finding people to talk to. Side quests. Fleshing out cities and industries. I think about a deep world -- something SNES games almost never gave.
I think about exploration and emergant gameplay, something SNES games almost never gave.
I suppose if your definition of depth is purely story based and can be fulfilled through a linear, one-story-fits-all game, then those SNES games can be deep.
It seems there is a disagreement as to what constitutes depth. If you want a "Sandbox" then most old-school RPGs will feel very shallow. You have numerous choices, but exploration and interaction outside those choices is limited.
On the other hand, if you want control over the story, many sandbox style games will feel shallow. Batman: Arkham City gave you a great sandbox with tons of things to discover and the story was fantastic. But your control over the story was minimal, limited to pretty much whether to do a side mission or not. You had absolutely no choices that affected the core story at all. Infamous 2 was similar. You had a lot of area to explore and interesting side missions, but you had only about 3 real choices and they lead to only 2 endings. The story was deep, the sandbox was wide, but your control was minimal.
I think there are great games on both ends (and in the middle) of this spectrum, but "sandbox depth (or width)" is very different from "story control depth".
There's also a lot of nostalgia based on the options available, and our expectations were much, much less. If we'd been given the option to play both, Fallout 3 would have been considered the more "immersive" experience without question.
I think about exploration and emergant gameplay, something SNES games almost never gave.
I suppose if your definition of depth is purely story based and can be fulfilled through a linear, one-story-fits-all game, then those SNES games can be deep.