My funny recent story about Audix mics....
I was mixing sound a couple weeks ago, and I went to put a 57 on the snare drum. The drummer said "Oh man, you aren't going to put a 57 on my snare are you? Where is the D1?"
I promptly replied "There is no way I would EVER use those over midrange hyped bullshit sounding mics on ANYTHING if I care about how it sounds. You will never see me use that crap".

The drummer replied "But that 57 has all that crappy sounding hi midrange" to which I replied "That 57 is the mic that has defined snare drums and guitars with most popular music for the last 30 years. It IS the sound for most Pop music" to which he said "But that is old technology. The Audix mics are NEW technology. Come on man, get with the new" to which I replied "Dude, when I hear anything new coming out that sounds worth a shit where they used Audix mics, and I hear a lot of it, I will then start to use them". Not much he could say to THAT!!!
This whole conversation took place with me forgetting that this drummer is a Outside Sales person for Audix....

The mics are made about 20 miles from where I live now (yes King, I got out of The Black Hole yesterday!). So, it made the whole slam that much better to say it to a guy that sells them for a living.....
Now, as to your request. I have used the D4 once each for micing a bass guitar speaker, and on a kick drum. For either application, it will work well enough. I would not describe the sound as "killer", "brilliant", or "stunning". Mostly, "average", "okay", "that will work for now" come to mind for kick drums, but for micing a bass guitar speaker, it actually sounded pretty darn good.
If you really play with mic placement and tuning the kick, the D4 will work very well for you. While it is nowhere in the same league as an RE 27 or RE 20, it is a better overall sound the a
AKG D 112, which is the sorriest sounding kick drum mic in 95% of the kick drums I have used it on. So, a D4 is actually a much better choice then a D 112, but I actually liked the ATM25 and
the Beta 52 better then the D4.
If you are getting it for cheap, don't even hesitate dude! Get that mic.
As to endorsing any of the other Audix D series mics. Well, you read what I think. You will find yourself eqing out lots of messed up midrange on those mics. They tend to have a sort of "pre-emphasised" sound for snare and toms, and that is the same concept as the D 112 for kick. I don't WANT pre-emphasised sound on drums. I like to TUNE THE DRUMS RIGHT, and use GOOD MICING TECHNIQUES for the well tuned kit to get my sound, not have a mic that supplies it nearly no matter WHERE you put the damn mic.
The D series stuff is garbage mostly in my opinion. The sales guys are definately exciting about pushing Audix for two reasons.
1- Audix is making a big push to cram their mics down peoples throats, so they have great price points for music stores.
2- Most of them like ANYTHING that has a SOUND that doesn't require that you think about how to use it. The Audix D series stuff fits right into what a music stores salesmen wants. A mic that sound great at low volumes and has a pre-emphasised sound. They usually like to take a better mic first, show how "dull" it sounds, then pop in the "darling" mic the are pushing with all it's pre-emphasised sound to amaze the sucker. It works with the NT1!!!
Anyway. Get that D4 because it is a far cry better then like a 57 on kick drum. After using it for a long time, you will find how to use it best, and I am sure it will be something you keep around for a long time to come, at least for certain applications.
It is nice to be back in Portland King! Vancouver (The Black Hole) just was not my scene.....
Ed