Hey Akarsh,
I'm not entirely sure about which Wolfson chip sounds better on the Nano, but I can offer up my experience, even though it doesn't overlay perfectly with your situation. Hopefully that will help you make a decision on your next move [if you haven't already].
I had an iPod Classic 6th Gen at 80GB. Like many people with that generation of iPod, the drive gave out on me one day at random - which I'm sure you've seen is both a cheap and easy fix, provided you have the know-how. However, as I began to research the best possible solution to fix my beloved device (had literally been everywhere from Carnegie Hall before a performance of mine all the way to Hawaii on a smooth jazz cruise), I decided to place it back in the original box as a keepsake. Why?. In my research on repairing it, I discovered a few things that were interesting.
The 5th and 5.5th Gen of iPod had a Wolfson DAC that was most friendly to higher end cans (like Sennheiser HD650, Shure SRH1540, although they would drain batteries and audio quality was not maximized). As it turns out (and anyone correct me if this information is inaccurate), Cirrus Logic purchased the technology from Wolfson and was contracted by Apple around 2006-2007 to integrate the new version in their line of iPods. The first DAC used in the original iPod Classic (better known as the 6th generation) had the poorest quality audio of any traditional iPod and did not have enough juice to power hi-fi cans at an enjoyable volume like it's predecessor. You'd have to use a custom amp, and even then, the sound was 'muddy' and 'dirty', even with FLAC (on Rockbox) or ALAC using the proprietary Apple firmware, which was version 1.2, I believe.
Now, how does all of this apply to you? Although I don't have any commensurate knowledge of the Nano line of DAC's, I do know that nearly any iPod (within it's own series) prior to 2006 had a superior sound to that of its successors. As you've [unfortunately] discovered, the new Nanos sound like garbage, no matter how you slice it. My guess is that the capacitors that work in conjunction with the DAC are very small in capacity - after all, that is one of the primary driving forces in sending a quality signal out to cans or speakers. If you research mods on iPods that can power hi-fi cans without an amplifer - which do, in fact, sound very respectable for a portable device - you'll likely find that soldering capacitors in line with the DAC fixes the issue. But, size is the primary concern with the newer Apple devices. Just look at the removal of the 3.5mm jack on the iPhone 7. With the newer Nano being shorter than previous generations that sounded halfway decent (4th and earlier, in my opinion), it's very likely that they cut down on the size of those capacitors. Check this link out (copy and paste for security <https://www.iflash.xyz/modding-audiophile-meets-ipod-diymod/>) to see a more detailed explanation of how the capacitor is integrated into the DAC and how tiny they actually are.
I would say in your case, to get back on track to listening to quality audio on the go, check out Amazon to find an iPod Video 5th, 5.5th, OR the iPod Classic 7th (160GB slim). Stay away from the other Apple iPods. Naturally, the Classic models get more expensive as you go up each generation, however, price is NOT a reflection of quality. It's a reflection of preference.
I have both the Video 5th Gen and the Classic 7th Gen. They both have an Apple OS, and they both only contain ALAC files from CD's that I own. I can listen to the same song on both iPods with flat EQ and they sound identical or completely different, depending on what kind of cans I have hooked up. For example, if I listen with my Bose Quietcomfort 2 or Sony MDR HW 700DS to a staple in metal grunge, Enter Sandman (Metallica), the 5th Gen reveals the merciless bass, while the 7th Gen does a better job of laying out the punch from the main riff. If I listened to both with Apple Earpods, they sound identical. For you, it's all a matter of choice. Personally, I prefer the 7th Gen, as I listen to songs that have more treble than bass and I enjoy being able to hear the instruments or singers individually as they fit within the ensemble. If I were a head-banging rocksmith or a dubstep aficionado, I'd have the 5th Gen by my side 24/7. It was said somewhere on this forum (I can't remember where) - the 7th gen has a more level-headed & precise playback while the 5th and 5.5th gen is more powerful with warmness as its base.
Ultimately, it's all in your preference.
Hope this helps!
-HL