They are too different to even try and do a direct comparison. The closest and fairest comparison would be amp 11 stock on 320 VS 340 amp 15.
The 320 in a simple wording, less lively and less analog fluidity in the while the 340 is also more dynamic with wider staging. These are very nuances differences. But if you cared much about analog quality, the fluidity, liquidity and performances, then the 340 wins hands down
The closest to 340 at the moment would have to be D16...but even that, they arr like a stark contrast to one another .... yet remaining similarly within a family
The D16 is like a Dad and the 340 is like a Teenager son.
D16 is warmer, more mellows, more dynamic energies, but also less airiness, less sparkles, a little slower in paces but still with all the details and nuances energies there are to be had...but thicker, denser.
340 at the moment is also very Dynamic but is faster pace, less dynamic energies density, more sparkles, more metallic textures when called upon, appear to be more energetic and more airiness. Vocal is especially crazily good on 340. Strings and bass instruments are tighter on the vibrations...which is the main differences between the mellower D16 vs more energetic 340.
I think it will come down to personal preferences. But IMO, I think Ibasso hit this 340 out of the park for these following reasons
1/ digital music that is clear, textured of high fidelity, correct tonality. Yet musical and realistic at the same time
2/ the fidelity in each timbres energies are unique to each instruments. There are no generalizations like other DAC. This have been observed by my ears since the dawn of the D16. This is why I keep repeating the analogues quality. No 2 Bass will sound alike, even playing under the same chord. The resonances and tonality will be set apart. The same as Eguitars and Acoustic one.
Even Dx320 and 320Max wont offer these uniqueness, which will be the main differences between these devices. All other Nuances are put aside
3/ a device of all in one, a DAP, slightly warm to the touch under operation and safely remaining inside the pocket or under a blanket. No heat threatening issues. Powerful enough to drive HD800s, additionally Desktop mode which further allowing more gain options and higher Voltage output available.
In my opinions, Ibasso continue to deliver the Digital cleanliness, precisions, quietness, accuracy of the digital worlds while reconstructing and perfoming music as it is, musical, emotional, connecting the artist to the listener, reminding older folk of Reel to Reel or Vinyl without all the crackles/pop/hiss....inconveniences of the analog mediums.
Is Dx340 better than D16 ? Yes and no, depends on your moods of the day I guess. But both are surprisingly equally amazing. Similar, yet different enough to have.
Now, If I had only 1 choice to keep 1 between D16 and 340. I will keep 340 only, due to the potential new amp cards with newer technologies. While I can be using LO toward PB5 for more desirable results. However, I will be missing the Daddy D16 afterward...

...nah, I will keep both