Inconclusive. The specs indicating reduced distortion and slightly increased headroom certainly seem good. That said, having used legacy 4060 (and 4061) for jazz, classical and whatever else music for the past 20 years, I've never felt distortion a big problem as long as they are powered correctly and the gain structure though the recording chain is right. There were a few times over the years that I had distortion with 4060 on High SPL deep bass heavy material, but was never able to rule out other causes such as batteries, or saturation of preamp or recorder input stages. That was a big deep organ classical event and loud rock subwoofer stuff, never had a problem recording jazz.
My take is that you should be more than good using legacy 4060 for jazz.. as long as the rest of your recording chain is able handle its output level.
I was similarly curious and eventually picked up a pair of Core 4060 a couple years back, intending to use them with the then new Deity PR-2. I previously used legacy 4060 regularly for classical and jazz, selected for its lower self noise and higher sensitivity than 4061, and figured the Core version would at least provide a bit more safety cushion even if it turned out I was unable to hear any difference. Alas, the output of 4060 proved to hot for the PR-2 to handle, ironically resulting in dramatically distorted bass as the recorder's input stage overloaded. So I reverted to using a pair of legacy 4061 I had on hand since its output better matched to the input sensitivity of the PR-2. Long story short.. I was unable to try Core 4060s successfully in that instance (and assume legacy 4060 would have had the same problem), and have not had a good opportunity to use them elsewhere since, much less properly assess the difference between the legacy and Core versions for myself.
Note that as far as Core goes, there are both Core (original) and Core+ (later) versions.
Core models are identified by a different color serial number band, and a tiny "Core" etching on the mic capsule.
Lets see..
4060 legacy - white serial number band.
4061 legacy - red serial number band.
4060 Core - blue serial number band.
Not sure how 4061 Core and the Core+ models are identified.