I honestly can't be bothered to read through 26 pages to see if anyone actually posted the correct maths here, so I will just do it:
Console - $500 Headset - $0 (you have it, so no cost) Adapter - $20 (guess) Live - $20 (using actual cost, for half a year to bring in line with the year's ps plus) Plug and play kit/rechargeable batteries - $20 (another guess, to bring in line with ds4 rechargeableness)
Total - $560
Console - $400 Headset - $100 (to give as good a headset for ps4 as you would have on XBO) Sale of included ps4 headset - ($20) (guess) Ps plus - $50 (assuming you can't get it cheaper, which sometimes you can, at least here in the uk) Rechargeableness of controller - $0 (it does)
Total - $530
Optional - PS Eye - $60 (depends on how much you would use kinect)
Total with kinect comparison - $590
It all comes down to how much you would use the kinect/eye. The batteries you cannot do without, and I presume you are a heavy online user hence the headset + online considerations, so those are pretty much essentials too, but if you are like many then the kinect is very much not an essential and can be ignored, in which case the ps4 is still cheaper.
If you were being super exact you should add some cost to the XBO headset, since if you were to buy a brand new ps4 headset it would last longer than your used XBO one, and the idea is to compare like for like as much as possible
Eg. If your XBO headset is 1 year old, and will last 3 more, and a new headset will last 4 years then $25 should be added to the XBO price.
I know the headset is a sunk cost, but the cost of replacement in the future is still relevant.
Source: I have a maths degree, and am a professional accountant.
Only one problem with this. Regardless of if he already has XBL active, you cant lower the price of lives yearly cost. If h has 5 months left, he'll just have to pay again in 5 months instead of 12. After 12 months it ends up being the same cost. Only case that my scenario doesn't work would be if he plans on cancelling live once the subscription runs out.
Add the remaining $30 to get to $50 for XBL and your example puts both systems exactly in line with each other at $590. Now add in the fact that the eye is totally optional and getting a better headset is totally optional, you can pay as little as $450 with your example (added in the $20 you deducted since I'd assume you'd keep the headset in that scenario.)
So... PS4: $590 with all options, but we have choice. This is assuming you actually buy a headset for $100. You can get decent ones from turtle beach for as low as $40.
Xbone: $590. Period. And that's only in this guys situation. If you don't have a headset, you're looking at about $650.