It seems like the porting team translated the analog control into something hexagonal which takes away a little control. When you control NiGHTS in the HD version you won't be as accurate as on the Saturn version with the 3D pad. This may not sit well with NiGHTS veterans but it doesn't break the game. It is still very playable.
My theory, and I've felt this since the PS2 release, is that the Saturn control pad was embedded in the controller, so controlling NiGHTS felt more fluid and *rounded* because the dent in the pad where your thumb rests is directly the fulcrum where the control is registered. Every other analog controller has been a stick mounted on that "ball" instead of being a literal "ball in socket." I think the fact that your point of contact with the controller is an inch away from the sensor, compounded with the fact that NiGHTS is an extraordinarily touch-sensitive game, is what produces this perceived disparity. (In 3D gaming, I can't think of any games more reliant on precision that frequently, NiGHTS changes direction constantly, most games played with these stick-on-ball controllers involve you pressing forward until you need to stop.)
I guess there'd be no way to determine this unless you could hook a Saturn 3D Control Pad to a PS2, PS3 or Xbox 360, but it's been my little theory for years. Hope I explained it accurately.