The jack on the Xbox 360 controller is a 2.5mm combination mic/mono speaker jack. I haven't tested this myself, but I've read that the pinout on the headset connector is mic/speaker/ground going from the tip towards the cable.
Microsoft doesn't really publicly specify the characteristics of mics that can be plugged into this port. No doubt there are some specs, so I can't say for sure that any generic mic plugged properly into this port would work.
When a headset is plugged into this jack, the game audio continues to be routed to the A/V connectors (ie, Component, HDMI, and/or optical) on the rear of the unit, but any voice chat audio is routed to the mono speaker jack on the controller. Without a headset, all of this audio is routed to the A/V connectors on the rear. Therefore, you can't plug a headset into the jack on the controller and turn the TV volume all the way down and expect to hear the game audio. Likewise, I don't believe you can plug in a mic and not a mono speaker to this jack without killing voice chat audio.
You can try to somehow mux the TV's (or your receiver's) audio into the voice chat audio in some fashion, but that can be a challenging DIY project. Just plugging it all together might work, but controlling relative volumes and signal issues/current flows might get awkward or complicated without at least a rudimentary knowledge of audio electronics hardware.
There are also third party headsets that handle this connection for you, and I've heard mixed reviews of such devices, so make sure you look into reviews of any specific models before you make a purchase.
What I personally use is an Astro Mixamp which is a wireless device that connects to the TV (optical), the controller, and a standard PC headset, and properly routes the audio around the room. You say you've already got a good Sennheiser headphone set - this is exactly the setup I use at home, a PC151 hooked to the Mixamp and my controller/the TV.
As per the FAQ,
Will the DUALSHOCK 4 controller’s 3.5mm headset jack support other headsets or headphones?
The PS Vita system’s headset is fully supported. Some other third-party headsets may support basic audio and chat functionality on PS4, but Sony Computer Entertainment cannot guarantee it.
So maybe. It depends on your headset. If it works in a Vita, it should work in a Dualshock 4 as well. As per this, the buds for the iPhone will likely work, but the best way to find out is to try. The compatibility concern is largely with Bluetooth and USB headsets.
It's not so much "capturing and recognizing" as that 3.5mm jacks with mic output (TRRS)(3 rings) are physically different than those without (TRS)(2 rings). If it has the ring to connect a mic signal, it will have a signal and if it doesn't, it won't. Signal v. no signal is pretty simple electrical engineering to sort out so that's nothing to be concerned about - headphones are already known to work. As per the vita headset working and the above information, so too should most 3.5mm headsets.
The concern with the mic is recognizing different implementations of TRRS because there are two standards (OMTP and CTIA) which have two rings flipped, but most devices nowadays have that fairly sorted. I'll test with an iphone's earbuds(with mic) at my earliest convenience and update the answer with results.
Best Answer
It depends,I used to have a ps4 afterglow headset I would use on my xbox one and it kept breaking so then I got the xbox one version and it hasn't broken since,if it's not specifically for the ps4 and it plugs into the ps4 controller then it should work fine with the xbox one,but if its wireless and it has a bluetooth usb with it and also has a little audio plug jack that you can use on other devices then no it would break because it would get worn out and would interfere. I don't know this 100% but I'm pretty sure it would be okay.