I don't have the D16 or PB5, but I listened to them and considered buying them. I really liked what I heard, especially in combination with both models. What stopped me from buying them was the lack of external power supply and the size of the stack. The fact that there are often direct comparisons of the DX340 to the D16 as a reference point in this thread clearly indicates that the DX340 is an exceptional solution.
However, I want to point out a different perspective here.
Here's my story (and a kind of summary): I was looking for a portable player almost obsessively and for a very long time. Along the way there was the DC Elite, DX180, DX260, DX320 (AMP 11 and 14), M23, R4, R6 PRO II, Onix Overture, XD05 PRO with many variants of opamps. I had the opportunity to thoroughly familiarize myself with the capabilities of the M9+, SP3000T, SP3000M and R8II. In short, these last four models did not blow me away. Of course, I'm not saying they're bad. It's just definitely not my cup of tea and I won't go into detail about why.
I was really impressed by the DC Elite. I would have never guessed that such an effect could be achieved from such a small device. However, it wasn't quite as convenient a solution as I would have liked. I decided that in my case, a DAP would be the optimal solution (provided that the sonics were as they should be).
The DX340 had been on my radar since the first mentions of this model appeared. I bought it blindly, in pre-sale, guided by both a hunch and the hope that I would finally get what I was looking for. I wasn't disappointed. Really. Such an organic tone obtained from a digital portable player and such defined technical aspects of this sound? Yes, the fact that I don't have a D16 or PB5 at my disposal absolutely doesn't keep me awake at night.
I think this is a great place to conclude.
If you need a player that you can easily take with you on the go, to enjoy a great sound signature and unlimited access to your favorite recordings at any time, choose the DX340. I don't think the DX350 (or rather the 360) will appear anytime soon. You will also get desktop mode functions. If I were to briefly characterize the DX340 signature: dense, detailed, dynamic, natural sound for pleasure.
If portability and convenience are not a priority, you can consider the D16 (D17 in some time) and the PB5. Of course, you always have to repeat like a mantra: it is a question of synergy and preference. Of course, you can buy anything if the budget allows it. In my case, the DX340 meets my needs in every aspect (I travel a lot).
Finally, I will only add that in my opinion the AMP15 is great as a stock amplifier. It's clear that I'll want to try out the newer modules that have been announced (and definitely the AMP14 that I kept after selling the DX320), but at this point I'd be guided mostly by curiosity rather than real needs.
It's really hard to make a mistake here, but you'll still need to verify it yourself