I already thought something was wrong. You probably don't feel like buying another Hori pad anymore but this one really is different. The hori fightpads I know of all have a 6 button layout. Hori also makes pad for shooters and other games maybe you bought one of those?
The Hori Fc 4 pad is different it is designed for fighting games. I am talking about this one below:
http://www.amazon.com/HORI-Fighting-Commander-Controller-PlayStation-4/dp/B00TKLFES8
They are sold out at amazon, but you can still buy them from ebay or maybe order them from somewhere else. The Dpad on that one is definitely even less stiff than the ps2 dpad and apart from getting a little used to the 6 button lay out(you won't even notice the 2 extra buttons after 2 days), the hori fc 4 pad is really the best out there right now for ps4 imo. It looks uncomfortable to hold like a normal pad, but the pad is bigger than it looks and fits really well when you hold it just like the ps2 pad. I was very skeptical at first too, but this pad is definitely ten times better than ds4.