Sony uses openGL iirc.
And even though they are likely too be similar we don't really know anything. Microsoft has more room than Sony to build a powerful console and its been rumored the next box will come in two amuse. One a proper console and the other one a Romulus with xbla.
Generally when talking about DX, people mean the feature set, not the exact api. I'm still gonna bet that the ps4 and 720 will be about the same box. I imagine that they will use a hex-core powerpc chip, 2-4GB ram, and a Southern Islands family GPU.
I would be shocked, honestly shocked if they are very much different from each other, hardware wise.