I've read that they try to keep it short. But on other sites and documentaries, it is said that they have to keep it long so that the birds don't look for food. Which is correct: short or long?
It depends on the type of bird and mammal species in native to the area and also the type of grass used in turfing; some of them may not survive if mowed very closely. FAA's Wildlife Hazard Management Manual concedes:
Species-specific responses may be expected. ... Airport managers need to work with airport wildlife biologists to determine what species of concern in regards to aircraft safety are in their area and what the habitat needs are for those species.
For most airports, FAA recommends a height of 5-8" of grass.
Considering bird, mammal and vegetation limitations, mowing at least monthly at a target of 5 - 8 inches may work in many airport environments as part of a wildlife hazard management program. ... Mowing at 5 - 8 inches should also reduce small mammal abundance.
You can find the link to the related Advisory Circular here: https://www.faa.gov/documentLibrary/media/Advisory_Circular/draft_150_5300_13a.pdf
See Page 101, paragraph B. Maximum of 6 inches in the runway safety areas.
Wildlife biologist generally recommend between 6 and 12 inches everywhere else on the airfield unless any haying will be done.
It is very important to authorities keep the grass cut, as we can see at Cork Airport (courtesy of youtube). Doing this, the airport signs can be seen clearly by the pilots, avoinding mainly runway incursions, and also keeping far, as much as it can, the birds and their nests. This previous measure sometimes does not work as we wanted, but it might help a lot decreasing the bird hazardous airside. After cutting the grass, the ground personnel will perform a runway inspection to clean it from debris.