As an end user; I've found BA's wifi to be pretty reliable even on long haul routes over bodies of land/water where you'd expect it to get choppy - like Bay of Bengal. The price isn't steep enough for me to opt not to on flights longer than 4+ hours.
Never had the unbridled pleasure of flying BA First. Happy to take gifts though.
The biggest issue with Wifi for me is reconnecting after losing it (for tech reasons, range, equipment - whatever). I've had a few occasions where I have lost access and had to pay again to regain access... I imagine the same issues apply in F.
I would also support multiuse devices instead of just phone; I'm usually a leisure traveller so I don't typically need multiple devices - however for the business minded being able to have work/private phones and/or laptop all connected would be useful - even if it meant a slightly higher price for your employer to pay whilst keeping you productive on the flight.