The Dark Knight Rises had a 4K master for the regular Blu-ray, so resolution-wise it probably won't be as much of a jump. The Batman Begins Blu-ray, while a bit soft, didn't look bad either. The Dark Knight, however, looks terrible on Blu-ray.
The footage from TDK shot on 35mm went through IMAX's proprietary upconversion process at the time called DMR when it was integrated with the IMAX prints. This process, sadly, involved some filtering and edge enhancement for the shots in 35mm. This would've been somewhat noticeable when watching the IMAX version in the theater (I certainly did). Since they wanted to replicate the IMAX version on the BD release, they likely used an IMAX print for the transfer. As such, ringing and other artifacts in the 35mm sections would in fact be accurate to the IMAX version. It probably would've been better to use separate scans of the 35mm footage, but that's not as big of a deal. The real issue is whoever mastered it added additional edge enhancement and noise reduction on top of
everything. Not only did the 35mm stuff get processed twice, the native IMAX footage got it's own dose of DNR and EE too when it should've been pristine.
You can actually see these differences by watching the Dark Knight prologue on the Batman Begins BD. It looks so much sharper and clearer without that additional processing. Further, the gamma and color timing is different from the Dark Knight BD. I don't know for sure if it's more accurate in that regard, but it certainly looks better and is closer to what I remember.
It actually wasn't even in the original Matrix. They added the color filter in Reloaded and Revolutions and then retconned it into the Bluray release of the original. The DVD version is still pure.
The DVD is definitely less wrong than the Blu-ray, but it's wrong too. Out of all the official home releases, the LaserDisc is probably closest to the theatrical color timing. There's a bootleg of a 35mm film print scanned at 4K floating around that looks quite different from both the DVD and the BD, but is fairly similar to the LD.
GASP! So he did shoot them digitally after all! LIAR!
But seriously, I'm pretty certain 35mm is capable of a higher theoretical resolution that 6K. Plus, at least what he's doing means that the non-IMAX scenes in TDK might actually turn out good this time.
IIRC, the theoretical resolution limit of 35mm film on good stock, scanned from the negative is a little above 4K at best. In practice, it's lower. The theatrical 35mm prints would often be lower still (sub-1080p). We've basically reached a point where the resolution of 35mm is maxed out. I believe 65 and 70mm is claimed to be around 16-18K though.