UPDATE: It looks like you will be able to carry over your profile, friends list and achievements to the Xbox One but the expanded friends list will remain on the Xbox one.
@Laughing__Man_ You’ll be able to use the same profile/friends list/achievements when you move over to Xbox One. ^BB
— Xbox Support (@XboxSupport1) July 29, 2013
It looks like your Xbox 360 friends list will not carry over to the Xbox One, according to the Xbox Support twitter.
The Xbox Support Twitter was asked if the 1000 friends limit increase would apply to the Xbox 360, they replied by saying that it will “remain as it currently stands.”
They were then asked what if someone was to recover their account on their Xbox One and then go over the friends limit that the Xbox 360 had. The answer was that the platforms would remain separate. “Your Xbox One friends list will be your Xbox One friends list. Your Xbox 360 friends list will be your Xbox 360 friends list.”
Major Nelson has also confirmed that cross platform party chat won’t be available to users.
@AceyBongos @Tullic @XboxSupport Probably not, since the systems use two different audio codecs.
— Larry Hryb (@majornelson) July 29, 2013
We have reached out to Microsoft for clarification on this and will update you if we get a response.