It's interesting that the line of Stewards all have different views of what exactly Gondor is. For Denethor, Gondor is it's people. He serves as it's steward, and is in contact with the various nobles and peoples of Gondor nigh daily. To Faramir, Gondor is it's culture. He spends his duties surrounded by ruins away from others, leaving him to admire the Idea of Gondor more than actual Gondorians. Boromir likely shapes his view of Gondor around it's soldiers. He's consistently on the front lines.
I think the division is more general than that. All these men participate in their societies and have lives within it, so I’d say their differences of meaning and connection and perspective are more overarching.
I would say Faramir is the one who connects to his people through the past. History and the idealism of it is what drives his sense of patriotism, as well as where he places himself within society. He looks at Gondor through the lense of (rose tinted) ancestors and what he believes their principles and ideals and lives were. Hence he’s very patriotic in some senses, but also gives a lot of thought to their perceived ‘decline’ and puts more value in the idea of Gondor ‘going out gracefully’, as in maintaining her nobility until the end. So he values historical artifacts and ruins like Osgiliath very highly and, I think, would have fought against the destruction of the bridge, even if he eventually conceded to aiding the plan. So Gondor’s unblemished memory of ‘greater days’ is his priority, which he extends to himself, and is why he’s so comfortable with sacrificing himself for those ideals, even though Gondor might still have need of him. They should go out gracefully, rather than make sacrifices to their honour to try and live just another day.
With this in mind, Faramir’s interaction with current cultural touchstones is very distant. He is more of a critic than a participant and keeps himself distanced from most of modern society, preferring older tales and discussing them at length with other high minded fellows.
Boromir on the other hand is entirely invested in the Gondor of right now. Boromir is connected to his people on a personal level. Gondor is certainly shaped by history but it's events and culture and society and the living breathing present moment of his home that creates the foundation of Boromir’s dedication, what he will sacrifice for. Hence he will sacrifice a great deal, his own morality, his own sense of goodness, they are things worth giving up because Gondor's breathing heart needs to be protected, deserves to be fought for, even till the bitter end. Hence Boromir doesn't see relics or places like Osgiliath as much more than a ruin or a battlefield, his connection to that city is certainly present but it's colder, more distant, it's a dead city to him and it doesn't represent much of the Gondor he's trying to keep safe for just a little longer.
So Boromir is very invested in modern culture, knows modern songs and stories, shows interest in modern fashion trends and participates in society as an active member, but cares very little for anything of the past unless it directly relates to his current interests.
DENETHOR is a mixture of both. He has investment in history, but in a more humanising way. Denethor engages with Gondor’s past and, in particular, his own ancestors, on a personal level and considers them carefully as humans with flaws to learn from. But he applies it to how to aide the Gondor of today, how to be the best Steward for the times at hand, and tends to remove morality from the question altogether until he is faced with a new specific problem. He is a keeper by destiny, and as a keeper he tries to hold all of Gondor that can be learned and seen, to put the country he knows into the perspective of what came before it. And he loves it all! Past and present, he wants to save all of it and keeps his priorities fluid, ever questioning himself, ever reanalysing the moment and situation.
But he also has other emotions tied to Gondor, a pride and dedication to his duties, but also a bitter resentment of them, of the necessities that it drives him too. Which creates this complex web of feeling and thought surrounding Gondor in Denethor’s mind, makes him sound jaded and bitter and offers so much meaning to the moment where he, on his own strength, snaps the sceptre of the stewards over his knee. Truly, Denethor has the most potent and complex relationship with his home and society and it makes it hard to keep up with his actions and thought processes at times.
