The stakes never felt higher in TDKR for me, simply because the movie jumped ahead for most of the siege. We never really saw how it affected the city, other than deserted streets, and a few people hiding in their houses. Even the revelation of the big Dent cover up never had any noticeable consequences other than Blake giving Gordon a flowery speech about morality.
In TDK, when Joker popped up and caused trouble, the tension always rose, and the **** always hit the fan. For example the build up to Joker crashing Bruce's penthouse party where we see Loeb get poisoned, the judge's car get blown up, Bruce choke holding Dent, that was proper edge of the seat stuff. You could almost see Nolan cranking up the tension meter when he was putting those scenes together with Zimmer doing that awesome score for it. Or when the Joker threatened to blow up a hospital if Reese wasn't killed, and we see the city go nuts, and several citizen attempted assassinations made on his life (even one by one of Gordon's cops). Even at something smaller scale like at Dent's press conference when we see all the citizens angry and scared because of Joker's reign of terror and demanding Batman be taken in (including seeing Bruce in the midst of it all seeing Gotham turn on him). It was more of a citizen reaction than we got in TDKR. I don't even have to go into detail about the whole segment of Joker allowing himself to be caught and the consequences that came with that. It all felt more raw, high stakes, and real than any of Bane's city siege to me.
Joker had the city proper scared, panicked, and we literally saw him turn it to chaos. Bane's big siege felt much more quiet and tame by comparison. Even on Batman lying with an injured back in a pit, that didn't compare to the despair and guilt we saw in TDK when he was hitting brick walls trying to nail Joker but nobody would spill about where he was because they feared him more than Batman. Or when he packs up his Batman stuff and prepares to turn himself in. Or when he's mourning Rachel's death and blaming himself for bringing madness and death onto the city. Or even the ending when he and Gordon are standing over Dent's dead body looking at what Joker turned him into and the mess they're left with. All felt more emotionally raw and bigger for me.