Here's one possible difference:
http://gimmegimmegames.com/2013/05/m...ram-for-games/
It's an old rumor, but PS4 was rumored to have 50% more compute units than the new Xbox One. That could be wrong, but it could also be right.
Some programmers have already envisioned a situation further in the life of each console where new game designs demand more out of each platform than the processing (CPUs and GPUs) alone can provide, so 8GB versus 5GB might well mean that the PS4 will be able to get away with considerably more in the way of precomputed assets, freeing up more time for the CPUs and GPUs to do work. And, even ignoring that, a 2-3GB difference in available RAM would mean that the PS4 will simply have more space to work with assets.
Another possible difference, despite efforts from some Forumers to outline a "BUT THE CONSOLES WILL BE THE SAME WE MUST ASSUME THIS" speculative scenario outside the facts, is that PS4 will allow used games and will allow you to use your games whereever you please:
http://www.eurogamer.net/articles/20...ock-used-games