Is the Batman of TDK trilogy the same as the older Batman in the Man of Steel sequel?

completely different

aside from early rumors and plans by WB to cross over Batman Begins with Superman Returns, Nolan and Bale were very Vocal that there was No room for Aliens in 'their' Universe...

-- there may be vague references to 'the clown', Batman's back injury, or Gotham being Cut off from the rest of the Country or some thing else, but since Joker is Batman's Canon Nemesis, the Back Breaking by Bane is from Knightfall and the cut off Gotham was 'borrowed' from the No Man's Land ... such references could be to the Comics as general back story, rather than Canon-welding to the Nolan-verse

This is going to be completely different. Batman from the Nolan movies was great, but he existed in a world which was meant to seem like our own. That's why his gadgets were mostly based on reality, and that's why none of his villains had actual superpowers. Man of Steel and its sequel are an entirely different situation, Superman, obviously, has powers, and Batman's character has to be modified to existed in a world that has more heroes and superpowers. I love the Nolan movies, but I'm going to stay optimistic about the new DC cinematic universe.