It's best not to use 1000Hz on Xbox One, the console can't handle it in some games. XB1 is designed for 125Hz input, whereas PS4 is built for 800Hz, so it doesn't suffer the same issue.
500Hz is stable on both PS4 and XB1 and should not create problems with the XB1 OS. However, 250Hz is the native USB polling rate for both consoles, though the XB1 controller only responds to every second ping.
IMHO, 250Hz should be the baseline for Response Rate if you want the most controller-like experience, while still taking advantage of XIM APEX's more granular mouse input. The leap from 125Hz to 250Hz is very noticeable. Going from 250 to 500 or 1000Hz is diminishing returns.
Personally, the only time I'd advocate 1000Hz input is in AA-heavy games that make hitbox entry difficult, like CoD games.
