In case you missed what I said Alock. Just talking about shinier graphics is one thing in terms of gameplay, but higher and smoother framerates directly affect gameplay.
Sure, you're right there and that is definitely far more important to me than graphics. The thing is, from my gaming experience so far, I've not had an issue playing fast-paced online multiplayers on my Xbox 360 - so it doesn't seem likely that it'd affect me hugely. However, I don't play shooters on PCs so I haven't experienced high fps rates on this genre in particular, maybe once I get my hands on both next-gen consoles I'll find that the more smooth PS4 really does make the shooting experience better. We'll have to wait and see on that one, but I don't deny it's a relevant factor.
The controller is going to be big for me - I love the 360 controller, and it's one of the big reasons I buy multi-plat games on the 360. The DS4 has been getting great reviews, but I'm still a little skeptic of the analogue placement for shooting games. The XO controller has been getting very positive impressions too, though it's not been used as much as DS4 (as DS4 has been released), the sticks are where I like them to be and the rumble triggers are meant to be brilliant by almost all accounts. I expect both to be good, but I may find that the stick placement on the XO controller + the rumble triggers mean I get my shooters on the XO. I'd place my money on preferring the Xbox One for shooters, but I can't ignore the great DS4 reviews.
Second screen facilities - if remote play works as well as the tech demos show, then this could be a big feature for me. I actually always play in my room anyway, and accessing my console is never really an issue. But still, if it allows me to play in my bed or on the shitter; perhaps I'll get games for the PS4 instead.
Connection - the reliability of Xbox Live has been huge for me, it's probably the most consistent online service I have ever used. Download speeds were much quicker, I found less lag on multiplayer games it was another factor for me. PSN is now charging for the service, and with the acquisition of Gaikai I expect the Playstation Network to improve in these areas and catch up with Xbox Live, especially since it seems Xbox Live will have some issues at launch.
However, if on the Xbox One some games have dedicated servers and lack on the PS4 - I'd say this trumps graphics and fps. A stable connection, with no host advantage and less delay between your actions and the replication on the server is very advantageous.
OS integration? We'll see about this one.. it's not important for most, and it'll probably be a while before it is to me too. The Xbox One version offers me more flexibility in my gaming, and could allow me to game at times when on the PS4 I wouldn't (lets say football is on or I'm awaiting a Skype call) then it's another factor.