That tree scene you're thinking of, while impressive, is also not what I'd call on par with Spider-Man. The tree was fallen over and in the middle of the road and while it was a big tree, I don't think it was a Redwood or anything like that.
If Azrael was a ten tonner, he would have beaten Batman worse than he already did, and he was still able to no sell Bat's best "board breaking" punches.
And if Batman used even an iota of Superman's true power, he could have one shot him without killing him or even causing lasting harm. Either Batman wasn't effectively utilizing his Kryptonian powers or it was PIS.
bane is actually pretty durable. Able to take a huge explosion in a warehouse or whatever point blank and able to walk out like it was nothing. I doubt Norman's punches won't do as much damage.
And as we saw in the last Secret Six arc, the SS were on Venom and taking on some of DC's most powerful heroes.
Gotta give respect where respect is due. Sorry. I don't write this stuff.
One more thing, but IIRC, Giganta tossed Bane around as well. Yet, Bane was able to walk it off.