If nidalee's cougar form had AD scaling she would be too strong. Even with AP scaling on her abilities but her Q (3.0 per total AD against a half-health champion!), she is able to drive almost anyone out of lane very easily by abusing her passive and auto attacks which is the main strength of AD nidalee.
AP nidalee has better wave clear and stronger lich-bane procs, but her damage is really unreliable and her lane presence is pretty weak compared to most over champions that go mid or top. She has really high scaling on her spear if you can land it properly though, and this compensates for her other weaknesses. Unfortunately, as the game drags on AP nidalee slowly transitions into more of a support character (granted, one with very high poke) than a damage dealing one, and there's also the fact that if you're close enough to use your cougar form you will probably die unless the other team completely ignores you.
The same kind of goes for AD nidalee too, her kit gives her little to no teamfight presence compared to other popular champions like shen and malphite (I've never lost to a shen or malphite with nidalee, though) and she has to rely on beating her lane to be relative past 30 minutes in the game.
In a competitive match, I'd go AD nidalee because I think she is a bigger lane bully than AP nidalee unless we're going for a poke comp, in which case I'd pick AP nidalee instead.
One final thing to note about AD nidalee is that I think she's completely outclassed by a good jayce. Assuming equal skill level, jayce will win the lane in terms of raw damage, barring jungler intervention. The good thing about nidalee, though, is that she has good sustain on her E which allows her to trade somewhat evenly with jayce -- however, even if you get a kill on jayce you will probably still be unable to push him away from the lane, and in my eyes if you fail to win your lane against a champion that has better scaling (jayce has much better teamfight presence) you've lost your lane, even if you go even in CS and kills.
Even with all her flaws, nidalee has to be my favourite top laner to play... I like how flexible she is, she can go pretty much anywhere and build whatever she likes and you'll still end up with a perfectly viable champion.
One final thing to note is that this thread is almost 3 years old, and nidalee was played much much differently before. I know that one patch her heal was buffed to a 1.25/AP ratio (wtf was riot thinking?) and her spear had an 0.65 ratio... nidalee with rageblade was the way to go back then (it still is viable now, it just isn't as strong as it used to be), and now if you build rageblade on nidalee you HAVE to get an advantage on the enemy laner because if you don't things are going to get pretty rough.
Just my 2 cents on nidalee
Small edit: there's a pretty annoying bug on her w, it's supposed to reveal bushes if you place the trap in it but sometimes it won't do that, and sometimes it doesn't show the full area of the bush (it does it other times)... it isn't really gamebreaking but it's just a very annoying bug.