Which headphones to buy

Hey I have a budget of $300 bucks for headphones. I'm considering the Audio-Technica ATH-M50x for $200
or the Phillips X2/27 at $250. I am personally leaning towards the Phillips. At my price point should I maybe go down even a little to Audio - Technia ATh-AD700X for $170 and get a $100 dac? Any recommendations on headphones you guys recommend would be appreciated as well.
Thanks

I've got a pair of Fostex T50RP that I am happy with, used a Schiit headphone amp and DAC with it.

For gaming I use an Arctis 7 headset.

Just remember any headphones with [iirc] anything over 35 ohm impedance you will want/need a headphone amp for it.

I am also looking to upgrade, though, and am curious as to others' suggestions. I hear good things about Massdrop/Sennheiser HD6xx, but I am not a fan of proprietary plug designs.

I have this, with the bundled DAC/amp. Love it. Don't know how it compares to other similarly priced headphones, though, or if that DAC/amp is holding me back much.

What's it like with an open-back speaker (or whatever it is c alled). Does the noise travel far? Never listened to a pair like that.

Yes, it does. If I hug a pillow with the speakers and stand outside my bedroom door, I can still hear it well. Not loudly, but well enough to bother anyone in the same room.