Edit: This is not actually true. I stand corrected.

The Kayak number doesn't include fees and taxes, whereas the Hipmunk number does.

Nope, from the the footnote: "Prices are per person and are for e–tickets and include all taxes & fees in USD."

Possibly due to a fare update happening around the time you did the search. When I do that search on Hipmunk I see a lowest fare of $899 (http://www.hipmunk.com/#!ORD_HNL,Dec28_Jan05@0,0) for a one-stop flight in each direction. Kayak's price is the same for the same itinerary.

Admittedly Kayak has one flight for $870 and a few for $896, but they involved two stops.