It depends on which headphone would be more convenient for you as well as what sound signature you prefer. Despite being from the same company they are actually quite different sounding from each other.
The ATH AD 500x and AD 700x are both open back and have a 3D wing support headband which use a self adjusting headband. While they are more comfortable than a traditional headband which is a curved piece of plastic/metal, they can be problematic if you have a small or narrow head. There is a mod using a rubber band to connect the two parts of the wing which seems to greatly help in that case.They also use velour earpads rather than pleather on the m50x( gets hot and sweaty fairly quickly, harden over time) and should be more comfortable.
Both are open back by design and are known for their airy and detailed sound. They are more like listening to speakers rather than headphones with an "in your head" type of sound. Since they are open back they will leak a good amount of sound and others nearby will be able to hear what you are listening to. Both are light on bass though respond well with an eq. While this might mean less immersion in games/movies positional queues such as footsteps should be easier to identify and pickup and they will work great for FPS games. They have a bright and aggressive sound.
Due to supply and demand and that the fact they're only imported from Japan prices are always subject to change. Right now the AD 500x (slightly lower end than the 700x, though the difference b/t them is small to begin with) are actually the same price.
The ATH A500x and A700x are closed backed versions of the AD 500x and AD 700x. They will have a larger quantity of bass and tamer treble at the cost of detail and soundstage.
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The Audio Technica ATH M50x has a similar sound to its predecessor, the m50 and what you are really paying for is the detachable cable. Note that the jack is proprietary and has a locking design, you can't use any 3.5mm cable with it. At its current price nearly $160 on amazon I would look elsewhere. If you are open to buying used the m50 often goes for around $80 or less which is much more reasonable.
They are closed back and will be better at noise isolation. They also fold up and will be slightly more portable. They have a slight v shaped sound signature... bass and treble will be emphasized while the mids are a bit recessed. A common sound that is geared towards your average joe and most would like it. Like they AD series they are very forward sounding... the soundstage is smaller than average and have an "in your head" sound common to closeback headphones. Out of the box they will have a high clamping force and the headband padding isn't the greatest. For longer listening sessions you might find them fatiguing due to their fit and sound. They shouldn't be hard to find in stores like Guitar or BestBuy if you are located in the US.
Both m50x and 700x/900x are easy to drive and you should not need an amp. A DAC will only be needed if you have problems with your onboard such as distortion, crackling, hissing ,etc.
These two reviews accurately describe the headphones mentioned above:
[video="https
/www.youtube.com/watch?v=LN6IrjXWRdM"][/video]
[video="https
/www.youtube.com/watch?v=NPd5BpEfNz0"][/video]
If you're open to other brands besides Audio Technica there are quite a few phones to choose from in that price range.