Im sure xbox one could do 4k. It would be a matter of changing the codecs in the software. With all of the processing power the xbox has, there is no way that it cant handle 4k even 8k. At this point also, I think Microsoft is gearing towards H.265 which will make processing hd video alot easier. You dont need to have a hardware chip to decode mpeg video built in. With the specs the machine has, it could do it on the software level. Also, sony could claim that they are the first, there is alot that Microsoft is holding back. I wonder what is going on with illumni room also.
Both companies have already confirmed that their boxes will support 4K for movies but not for games. I don't know where the earlier poster got that PS4 will be the first player to support 4K though. Both say they will support it but I haven't seen either claim that they will be the first blu-ray player on the market to support it.
My guess is that as soon as the official specs are released and movies start being sold in 4K both boxes will be updated to support it and many other stand alone blu-ray players that support it will be released. I highly doubt that movies are going to start coming out in 4K and there is only going to be one box supporting them for any significant period of time.