The XBOX could be beaten for $500 easily, though the PS4 is another story. I'd say $800 like what the person above said, though there will be some things the PS4 has which you wouldn't with that budget.
In terms of game performance the PS4 contains a GPU with apparent performance in the range of a GPU like the HD 7850 or GTX 660 ($150), though with the optimisations they have due to very low-level programming (lower than the Mantle API releasing) it could end up having performance similar to an AMD 7950 or even 7970 ($300+) according to Sony, though it's speculation for now. As for the XBOX you could get a comparable GPU for slightly higher than $100. These are US prices I'm talking about - it may not reflect your location.