Well, the bulk of my listening is Jazz and I've been vacilating between MP3 and AAC as my codec of choice. My reasons for considering MP3 are compatability. (not enough room for lossless, and what if the moon turns blue and Zune is actually an excellent MP3 player) My reason for choosing AAC is, well, my iPod.

Anyway, I was leaning towards MP3 since its the one format that is supported by just about every player on the market, including the iPod. But, then I discovered this sample:

Tumpet sample

And I could quite easily ABX the sample up to 192 VBR LAME. AAC had its problems with this sample also, but they weren't as obvious and I had a much harder time ABX'ing it.

Any other Jazz fans on the board? What codec and bitrate do you use? And remember, I don't have high end equipment or golden ears. (I used the apple earbuds for my ABX'ing.)

I use 'currently recommended version' LAME -V0 --vbr-old just to be on the safe side - didn't notice any problems so far . The bitrate rarely goes above 250 kbps.

Trumpet is one of my standard problematic samples (harp40_1 and herding_calls are the other ones) which I appreciate a lot cause they are all tonal samples which one wouldn't consider easily to provide trouble for many encoders when listening to the original.
Past time's Lame VBR (prior to 3.98a3) behaved pretty badly on these tracks, but it's not just VBR that causes the problem, especially the 3.97 branch of Lame didn't do a good job on these samples.
Current Lame 3.98 alpha development however is about to improve a lot, and especially 3.98a6 is excellent on trumpet.

Though I'm very glad about 3.98 development, current 3.98 alpha is not yet entirely at the end of the road.
So as for best quality IMO it's still best to use the best encoder version and setting known so far to achieve at the goal.

As for my best knowledge there are three things to consider:

1) choice of average bitrate
According to intensive listening tests on various mp3 encoders I found that I have to use an encoder setting that uses an average bitrate of 224 kbps or more to get these samples to a totally satisfying (to me) quality level. The only exception to this was the Helix encoder which gave very good results to me at a VBR setting which takes 205 kbps on average (level's setting - see Helix thread).

2) choice of CBR, VBR, or ABR
There's a rather high risk that VBR can be fooled by samples like the one I've tested. Within my test this was true not only for the older Lame versions I tested (up to 3.97), but also for the Fraunhofer encoder I tested that provided for VBR.
CBR quality was much better than it's reputation, and in fact CBR 224 gave very satisfying results.
My personal favorite is ABR because of it's wider variation of audio data bitrate compared to that of CBR, but my test did not prove it superior.
In order to provide for a safety margin, I personally use ABR 270 kbps. But this is only a matter of taste - anything around 256 kbps no matter whether using ABR or CBR provides for excellent and robust quality when using an appropriate mp3 encoder.

3) choice of mp3 encoder
My personal choice is Lame 3.90.3 (or 3.91 which is essentially the same thing). The current Lame 3.98 branch however is about to improve a lot so I keep an eye on it switching over as soon as it makes sense to me. Helix encoder or Fraunhofer encoder (for instance from WMP10) seem to be very good encoders as well.