Shure SRH440 vs Onkyo W800BT

Sound signature is fairly neutral, with slight elevations to the bass, mids and highs.
Bass has a nice fullness to it, with some extra depth which gives the sound a lot of body.
The mids are neutral but slightly forward, making the vocals sound really clear. Aggressive guitars can sound a bit harsh because of this though.
Treble has good extension, and the added peak on the highest frequencies add more sparkle to the sound.
Overall, these headphones can be used both for critical listening and for casual music enjoyment as well.

The closed back, over the ear design blocks out a significant amount of noise, allowing users to easily focus on the audio. Sound leak is also kept to a minimum.
These are great for tracking and monitoring, and are also great choices for use in quiet environments like a library.

You can easily remove the cable when these are not in use, making them easy to store. This also makes the cable easy to replace when needed.

Instead of being bloated and overpowering, the bass is punchy and fast so while these will not be able to produce a lot of rumble. Thump should be satisfying for most users. The highs are nice and airy with a lot of detail yet never become harsh, so these are not fatiguing to listen to. The mids sound very natural and jump out just enough to make vocals and guitars very easy to hear and appreciate.

These should work best for more vocal and instrument focused genres like jazz, rock, classical and the like. Bass heavy tracks will still sound good with these, though these headphones will not be able to give the deep bass that bass lovers will be after.

The carrying case has an internal battery, and with a full charge, can supply the headphones with 5 full charges on the go.

The soundstage that these produce gives the music an open feel with good instrument separation. This quality will help give the listener an immersive music listening experience.