Which processor has better audio for home theater?

Well, the first three are simple to differentiate.

The Statement D2 and D1 are identical except the D2 has the added video scaling, so a tie, the AVM 50 is lower down the line and not as heavily powered (supplies) so a little less.

Comparing to the Krell is a matter of taste, let your ears decide.

Don't dismiss the older Anthem AVM 20's and 30's. They can be fully upgraded to the AVM 50 (HDMI) and sound just as good if not maybe a touch better (at least to my ears.)I think it's like $2200 for the upgrade and the AVM 20's have been selling for around $1100-1200. That would allow you to get into the AVM 50 for about $3400(better than $5000!) The AVM 20 has had several upgrades up to now (it's something like the 2.21 version.) The older AVM's were well reviewed and a lot of peoples references. They are excellent on music (except I'm a firm believer that NO processor will equal a good 2 channel preamp using music.)
The other thing is no higher end processors due the new codecs(like Dolby True HD, etc.)

Krell HTS 7.1 for HT, but even more so for 2-channel. This is a great processor and at the price you can buy them for brand new with the full 5 year Krell warranty for less than $3,000 (vs. the $8,500 LP), it is a true bargain.

I listened to both the Anthem D2 and the Krell and ended up buying the Anthem. I found the Krell a little bright, but that may have been the speakers that I use as well (B&W 803d, HTM1 center, rears are the equivalent to the 804s in ceiling mount, I forget the designation). I also use the Anthem A5 amplifier. I use the system about 50/50 for music (both digital and analog) and HT. Video on the Anthem gear is fantastic as well.

The HTS 7.1 is not going to smooth things out or roll off the highs (Vayjay, I am NOT saying the Anthem does this FWIW). It will convey the signal without adding much of anything (in direct preamp analog mode) or taking much of anything away from the music. I like the HTS 7.1 because it is the only Pre/Pro that I have listened to that can do a very good job on 2-channel (*I have not listened to the Anthems). By the way, my system would be proclaimed by a lot of people as having a very bright potential - Krell FPB amps and Wilson W/P speakers with a GNSC modded Opus 21. I can say my system does NOT make anything bright sounding, but a bad recording can be bright if that is in the recording - my system will not roll that bad recording off.