Wow. I dreaded coming into this thread, half expecting **** like "Can't we go five minutes without comparing the two

" and other *****fits. But it's been completely civil. Therefore, I'm proud to lend my two cents.
1. Both have Bats, Joker, and Harvey.
2. Both have stand off confrontations in the street where it's basically just, Joker and Batman.
3. Joker's takes control of the mob.
4. Joker ****s with Bruce's love interest indirectly.
5. Hell, both films have an Eckhart involved.
There's alot of other similarities just shots wise in that video. It didn't even dawn on me that the shot of bats on the roof was damn near the same as in 89. Also the clip with the batmobiles doing the exact same thing in the exact same way in the shot was crazy. The parallels are definitely there.
Some great additions (especially the clever Eckhart one). Look, this exercise isn't about making value judgements, at least not from my POV. It's merely about drawing parallels between the two films in which Joker appears.
Having now seen the entire film (I went to the Nyack preview), I can add a few more comparisons (spoilers!):
1) Both films, near the end, depict Joker plunging from a building. In both films, Batman is the reason for his fall, and in both cases, this is how Joker is finally subdued.
2) In both films, Joker takes over a TV broadcast to send the public a message.
3) In Burton's film, Batman tells Joker 'you made me'. In TDK, Joker tells Batman 'I need you.'
4) Both films involve a swing in public opinion toward the Batman. In Burton's film, it goes from fear and suspicion to trust and acceptance. In TDK, it goes from something resembling trust and acceptance to fear and suspicion.
5) Attitude towards money plays a role: Burton's Joker gives money away. Nolan's Joker burns it.
6) Gordon's life is explicitly threatened in both films. RELATED: Corrupt cops place lives in danger in both films.
7) A major character's face is hideously transformed in both films. In both cases, Batman is involved (though not really at fault).
8) Early on in both films, Batman is filmed in an unusual way - from above. In both cases, he witnesses the escape of criminals below him, and moves down to apprehend them. (This happens only twice in the Batman movies, and these are the two instances.)
9) In TDK, the Batmobile pursues a Joker-painted vehicle. In Burton's film, I believe it's a Joker-painted vehicle chasing Batman.
This one is subjective: I could swear that, in one or two statements - Ledger sounds EXACTLY like Nicholson. Now, this Joker modulates his delivery all over the map, and has a wild variety of speaking styles. Since I do not (yet) have a TDK DVD, I can't pull a clip for comparison. When you see the film, just listen carefully and see if you can spot this. I think it was 3/4 of the way through the film when I noticed.
I'm sure there are more such parallels, coincidences and contrasts that astute fans will pick up on.