I’m sorry to be Mr. Picky, but neither one of the models you’ve mentioned features active noise cancelling. Rather, they passively isolate sound thanks to their leatherette pads and closed back design.
It’d be great if active noise cancelling features made their way into more gaming headsets. In all my years down this rabbit hole the only two I’ve found on the gaming side that have ANC are the Turtle Beach Stealth 700 and Elite 800.
I discuss the isolation characteristics of the two you’re looking at in each review, and they’re both on the stronger side of the spectrum as far as passive noise blocking goes. So I’m not sure either one is a great choice if you don’t like feeling too closed-in/want to hear your voice.
If you don’t want to buy an open back pair but still want to monitor your voice, you’ll perhaps want to look for a headset or DAC/amp that features Sidetone. Sometimes it’s also called real-time mic monitoring. This is built into numerous headset products, though most of them connect through USB since the sidetone is powered through their internal DAC hardware.
Neither of the headsets you’ve mentioned have built-in sidetone.
A number of standalone desktop mics also have this feature, like the Yeti series from Blue. The Xbox One features built-in sidetone as well, if you play with a headset plugged into the controller. Hopefully, Sony will do this for the PS5/whatever it ends up being called.
A few open back headphones do have solid, accurate bass response that digs down deep. Both the DT880 and DT990 have wonderful bass performance. And the Sennheiser HD559 is solid in the low end as well. But those are the exception not the rule, and I’m right there with you in that I also tend to prefer closed headphones.
Hope that all helps you out somehow!