It doesn't feel 100% identical. I have both an original pad, the SNES classic pad and the Buffalo. All buttons except the d-pad feel very close to the original. However, the d-pad feels quite different. The main difference is that the travel is quite a bit longer. It it quite obvious when you're rocking your thumb back and forth on the d-pad. It's not a huge difference, but it's worth mentioning. That, and the fact that many of these controllers have phantom d-pad presses, probably due to bad electrical design. I've tested four and three of them had this issue to varying degrees.
For me it’s quite obviously the other way around. I have a well worn original pad and the d-pad is completely mushy and non-distinct. I've got a bunch of SNES/SNES style controllers here (original, SNES classic, Buffalo, Cirka and Retro-Link) and the classic pad is by far the springiest feeling of all of them.