I get along famously with My Sennheiser M4 over the ear Bluetooth phones. I use a Now discontinued LG V40 phone as a source. Given that my 76 yo damaged ears suffer from tinnitus and loss of anything above 6 to 8khz, This combo is great for my needs. Noise cancellation has really improved significantly over the years and as ghdprentice points out, ambient noise ruins any attempt at hi fidelity in a travel environment.
I usually utilize the Bluetooth AptX for listening when I walk. If I want highest possible fidelity, I purchased aTempotec Sonata HD Pro DAC/Amp that's capable of 24/192 resolution with wired phones. With above said ears, I don't really detect much difference. The Sennheiser smartphone app also allows for sonic tweaking so there is also that.