Technology

Okay so this provides an interesting set of restraints as they are traveling headphones. I have yet to find what I consider the perfect traveling headphones but there are a couple I have found that come close.

The Sony WH-1000XM5 and the Bose Quiet Comfort Ultra's

Bose has some remarkable ANC, after all that is one of the things that really established their name in the market. My main two complaints with the Bose is the sound signature isn't always the best (IMO) and that the app can be finicky at best bordering on terribly annoying.

The Bose Quiet Comfort Ultra's are really amazing for the ANC and their sound is improved with their new processor but if you are on an apple device you will miss out on this feature. Only devices with a snap dragon 888 or newer can take advantage.

One of the caveats is that the microphone quality is not the best I had some complaints about call quality when using the Bose.

One pro is that they collapse into a smaller form factor with a slightly better carrying case.

For the Sony XM5 I really preferred the sound signature and styling is just Chefs Kiss. They fold flat enough which makes packing them easy enough even if they aren't as small as the Bose. I also prefer that the XM5 has a 3.5mm audio jack instead of a 2.5mm on the Bose. It feels more likely to last longer. Also because they are slightly older you can probably find a better deal.

The Sony does a remarkably good job at rejecting background noise when making phone calls and has a much wider band of frequencies captured. The Bose sounds very tiny and scratchy.

The Sony also has a longer battery life which is nice.

I know you said that outrageous good noise cancelling is key but if you are willing to compromise a little on the ANC quality the Focal Bathys have far superior sound.

The frequency curve on the mids to low end is practically flat, it does fall off the tiniest bit on the upper mids and lower highs but for me this means you get a really accurate sound reproduction that isn't tiring and can be listened to all day long. The soundstage is really wide especially given that they are closed back.

The looks are a bit odd and they are a bit on the larger side. They still fold flat and they have a superior amount of cushion and I think the build quality is better.

Oh if you are a bass head that just wants super punchy powerful bass go for the Sony's over the Focals. The Focals are more accurate but less present.

Lastly is my currently traveling setup. Its... non-traditional. I am using a pair of Samsung Galaxy Pro 2 buds which really fit my ear well and already have some pretty remarkable ANC. Not nearly Headphone level but still very good. Here is the non-traditional part: if I REALLY need to block out outside noise IE on a construction site or in the shop I wear the buds underneath a pair of passive cancelling earmuffs. Specifically the Peltor X5 Earmuffs.

It's not stylish but the Earmuffs + Buds + Comply Foam tips feels like you are in a void. Barely have to touch the volume to hear your music as clear as day.

OK, there are many different ways to approach your current setup.

Wired vs wireless isn't that much of an issue as you can get very affordable Bluetooth adapters for your computer.

Also the goal of what you want your headphones to do is going to come into play here as well because you may want a stationary setup vs mobile.

Then there's the microphone requirement...

Actually rather than fill an unrelated thread with headphone advice I'm going to DM you.