A lot of cod heads switching to the ps4 will be upset as far as the network go. I've always say COD and SF games always run like shyt on PSN and now both franchises have exclusivity deals with Sony
"PSN" doesn't have anything to do with a specific game's online connection. If a game is laggy, it's most likely bad netcode on top of that it's running on P2P connections which this beta mostly is. BLOPS3 HAS dedicated servers but the beta is limited on that right now.
As far as lag goes, most people last gen on PS3 were probably using wireless vs wired and on 360 you pretty much only had wired connections so that would make a difference on some fronts. Even then that doesn't solve shytty connections on the users end. Ever played Halo reach? 4? Gears ? They all had hella lag, even COD. To say that it's fine on Xbox 360 is just being disingenuous.
Xbox live doesn't make "good" connections out of thin air.
COD:AW on XB1 with lag.
TL:DR
LAG is a result of a lot of variables. Thinking "XBL" or w/e solves that is just stupid and ignores the laws of physics.