Best high-end headphones with noice cancellation ...

The Sony's are the best from reviews and personal experience. PSB good Sony better.

I know, looked at those as well, but just have the feeling they are much "plastic-like" ... maybe not .. 

I like the Sonys. Fidelity will depend on what you're using them with. Android devices support LDAC, the bluetooth codec with highest data transfer rate. Apple devices do not, nor does Windows. But, the headphones can be used wired.

Would be using them with an iPhone 11 or on an iMac. 

I asked a similar question a few years ago and was convinced by the responses that instead of looking for headphones with active noise cancellation (ANC) that sounded better than my Bose over-ear I was looking to upgrade from that I’d be better off with the passive noise cancellation from a good set of IEMs. IEMs will be much smaller for your carry-on or to tote around town and Shure (for example) advertise 46dB reduction in outside noise levels.
The noise reduction is definitely different from ANC in that it is across the spectrum and all frequencies with good IEMs as opposed to ANC that often works best only with constant background noise (like airplane engines or the lawnmower) but works less for sudden sounds that aren’t constant which instead sound muffled/wrong but definitely get through. 
I ended up with a pair from Campfire Audio and love them, but there are lots of IEMs that will blow away the best ANC headphones for sound quality at the same price. 

If you’re committed to ANC, the Sennheiser Momentum True Wireless 2 are often said to be the best of the ANC IEMs for sound quality if the small and travel-friendly form factor of in-ear is important...haven’t heard them myself.

Actually, this would be my first ANC - in case I go for that - I am used B&W P7 wired without ANC 

I’m not a huge Sony fan, but I have to say at around the $300 price level I’d go with the Sony WH-1000XM4 for it’s all-around solid performance. That said, I just bought my wife a pair of Sennheiser PXC 550-ll for $200 for Christmas that seem pretty comparable but not quite as good noise cancelling as the Sony. I’ll report back on sound quality when I get to hear them. Won’t buy Bose. Hope this helps, and best of luck.

One last thought I’m not quite sure about, but the Senns offer a wired connection that allows for lossless quality, and if you can stick a DAC or DAC/Amp in there (like an Audioquest Dragonfly Red) so much the better.  This would push me toward the PXC 550-ll for the potentially higher sound quality if it’s valid. 

Yeah, also looked at the Sennheiser ... was told thought that the sound is quite metalic ... 

With respect to traveling, I have had several pairs of in ear IEMs and also active noise cancelling headphones including Sennheiser and Bose for long haul flights, working, listening to music and / or watching movies.
I loved a pair of JH Audio IEMs which were custom made and wonderfully comfortable.  I get, however, a certain claustrophobia with even the best and most comfortable IEMs that I do not get with active noise cancelling headphones.
Both types would be good.

Business flyers buy Bose because that is what they do.Music lovers usually buy Sony .

The ever popular Bose QC35 II (8/10 WIRED Recommends) remains a fantastic noise-canceling option, but Bose’s newest flagship headphones, the Noise Cancelling 700, take our top spot for business users. They have excellent noise reduction that quiets clacky keyboards or chatty roommates better than ever, plus slightly better sound quality and battery life than the QC35 II MCDVOICE

Yup.  Bose is much better at cancelling sound than reproducing it — that’s for sure. 

Been a BOSE user for years and years and they sound surprisingly good. Had been considering a switch to Sony, but they had call uses (I used multi-use when travelling). Now that they have fixed that from the latest reviews, I would buy the Sony.

Sony WH4’s.  Just bought (and returned) a pair.  The noise cancellation is great, they are super comfortable if they fit properly (the were hitting my right ear funny so I took them back.  This was more an issue with my ear and not the headphones).  
They sound pretty good once eq’d from the phone app.  They are waaay too bass heavy with the eq set at flat.

Phone calls sound great, the bluetooth has a wide range, the battery life is pretty good... for active noise cancelling, wireless, phone call, they are probably the best.  The build qualityisgood and even though they are mostly plastic, they do not make any creaking noises.  They are on sale now for $300.
My problem is being totally dependent on the internal-electronics within the headphones.  They do sound better hardwired to a nice headphone amp / dac but only with dsp turned on.  With no dsp turned on and the headphones plugged into a headphone amp, they sound like $5 headphones.  Absolutely horrendous.  Turn on the dsp though and they sound pretty dang good.

The ultimate problem for me though is how close they are in price to the Sundaras (open back planar) and the Shndaras should blow the Sonys away.  And if I were going for noise cancellation I’d go passive noise cancellation and get a pair of planar in ear monitors ghag sojnd superior to the Sonys for have the price.  Again though, comparing apples to oranges.

The sony wh4 is probably the best at what it does!

I have the top Grado in ear wired wonderful.   I haven't heard their new wireless, but I'd listen to them.  I thought the Sony 1000 was very restrictive...

Thanks for shearing this post. This is very helpful info.

Late to the party..
BOSE and SONY came out top, and I spent quite a lot of time trying to justify paying the price of the BOSE ones (I went and tested both, in different environments), but in the end I couldn’t. I got the SONY WH1000XM3 headphones. Marco (from ATP) has a pretty good list of bluetooth cans to refer to.

IEA, noise cancelling no matter what the brand are junk and I have had them all. Bose, B&W, Sony....... pre Pandemic I flew every week. 

If you are using iPhone then Apple’s new headphone Air pod Max would be a good choice I never hear them but do have there AirPod Pro. And to my ears the noise cancellation is about the best that’s out there and nothing tops there transparency mode. What I use is the Sony wi1000xm2 and there pretty good sounding earphones, but in transparency mode there not in the same class as apple.

Hello! For me, BOSE and SONY headphones are the best in sound quality and design.

Build quality on the Sony WH-1000XM4 is poor.  My pair’s headband broke after a year of moderate daily usage.

Hello. And how about Shure SRH840? What do you think about this model?

I went to can jam in New York pre pandemic just to listen to all the anc headphones that were at the show. Listened to every offering in the hall and ended up buying the sennheiser pxc -550.  Bose did not exhibit at that show and I have their first generation anc cans, not very good sound but good anc. I was surprised I ended up with the sennheisers but they sounded best to me over the Sony’s and all the other brands. I think headphone sound is very person dependent because of head shape and personal preference. The pxc 550 have great battery life and good Bluetooth connection. I use mine with a iPod touch so I would assume they would work well with a apple phone.  Nothing better than putting them on your head and getting to listen, I was surprised at the difference in sound from all the different brands.

Hi there. I'm searching for headphones which also don’t leak sound for other people. Did you have some such models? I saw interesting list on the site, maybe you can share your reviews about these headphones.

HarmonicDyne Zeus .Open Back Headphone .Hi-Res Crisp Sound.Very Wide Sound Stage . So,I do think it will help you to use for longer time

Your going to think I'm nuts but give the Cleer Flow II's a shot.  They're on sale for Father's Day at $150 right now, normally $200 and they are a performer that punches way above their weight.  Check out the latest review from April 30th, https://www.soundphilereview.com/reviews/cleer-flow-ii-review-12933/ and from Forbes in February,

https://www.forbes.com/sites/marksparrow/2021/02/09/these-cleer-flow-ii-headphones-sound-superb-and-cut-out-most-distracting-noises/?sh=1b2ed1755f7b

Maybe you could try some TWS headphones, like Bose, Sony, Beats... If your family likes sports, you could also try bone conduction headphones like Naenka, AfterShokz...

Sony’s flagship Sony WH-1000XM4 is the successor to the WH-1000XM3 and brings support for multi-device pairing, surprisingly effective DSEE Extreme audio upscaling and auto on/off. However, the primary reason to pick these headphones is of course the exceptional noise cancellation. Mcdvoice

The Sony WH-1000XM4 is regarded as the best noise-canceling wireless headset on the market. The Sony WH-1000XM4 features the greatest Bass system, and it also retains both performance and appearance.
These are a cordless pair of headphones with a built-in Bluetooth capability. These headphones are more reliable because they do not have tangled wires. The Sony WH-1000XM4 is worth purchasing because to its small weight.