I haven't had any problems at all with COD WAW. Games normally load properly, and I have no problems. I haven't played it in a while though, so I don't know if the update killed it off slightly. I have a pretty quick internet speed, and it's not wireless. I only have one other computer running from a router too, so it's not under much pressure.
There's no technical reason why Xbox Live would be any quicker than PSN. It may be written slightly better, to reduce processor cycles over PSN, but no way would it be noticeably better on the same connection. Lag is determined by your internet connection strength, processor speed (where the PS3 beats the Xbox hands down), and the servers used (which depends on your ISP).
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