The two systems have nearly identical specs:
-- Both have the capabilities to run both DVDs and Blu-ray discs;
-- Both have 8 GB of ram;
-- Both are using eight-core processors by AMD;
-- Both contain 500 GB hard drive;
-- However, the PS4 hard drive is user replaceable (upgradeable), while the Xbox One does not have a user replaceable hard drive, but it does support external storage.
The Xbox One has been looked down upon since their poor showing at E3, but have changed a lot of what was previously said. Previously, they said that they would restrict used games, and require internet access, but now they have changed that, and allow used games, and do not require internet. Also, they do not require their peripheral, the Kinect, but it will still come in the package, thus being one of the reasons that the Xbox One is $500, instead of $400. Factoring in the cost for Xbox Live, the Xbox One is going to be more then $100 dollars, if you want Xbox Live capabilities. User polls have indicated that they are going to buy the PS4, but prefer the Xbox One controller.
There are many things that you should think about before choosing a system. Price, although you said it doesn't concern you, if you would actually use the Kinect, the controller, etc. If most of your friends are going to get the PS4, maybe you should too? Also, if you are looking to game on the go, Sony has been advertising the PS Vita as the perfect accessory, while the Microsoft has not created that. One last thing to consider when buying the system is the exclusives, such as Halo, Forza, Killzone, etc., for the PS4 and Xbox One systems respectively. Basically, choose what suits you better.
Have Fun!