The Xbox One is going to be weaker than the PS4, but the 360 is weaker than the PS3, so that's not really that big of news. Third party games will probably look identical on both systems and first party games will probably look slightly better on the PS4.
I'm not sure how true this really is, the consoles are almost the same. I guess by a very thing margin the PS4 will be a hair more powerful, but it will also have to go through an extra line of code because most games will be written for the Windows Kernel for PC and XBox and then be ported over to PS4. It's no where near the issue it was for the PS3, where it had very different architecture, but may make a difference when we are talking about that 'hair'.
They both have 8GB of RAM, though XBox has partitioned off 5GB for games and nobody knows if Sony has partitioned off any of it's RAM at all. I don't think this will be noticeable right away, but a few years down the road when games start pushing RAM like they have for last few years on current consoles, those partitions may make a difference. The PS4 has DRRM5 and XBox has DRRM3, the five is a bit better and dumping bigger loads (uh heh, he said dumping big loads) of info where the three is a bit better dealing with graphics, plus the XBox chip has another 32mb of RAM on the chip just for graphics.
Another factor that could play a role is the whole "cloud" thing. XBox is talking about games using it during gameplay and going forward using it to make the console more powerful, so it's not just going to be for game saves. They also have a huge load of servers going online for the new launch to support it. I'd really like to know more details on how they plan to make use of the cloud, but that could be a difference in power as well.
I'm really interested to see some benchmark tests (but we probably wont until release or right before). I think games are going to be the big difference maker. Whatever these dozen exclusive XBox titles they have announced better be good and they better make a big splash with them at E3.