The PS Vita 2000 has the most satisfying and precise D-pad I've ever encountered.
It's a single plastic piece, but unlike every other Playstation controller, it doesn't feel stiff. The buttons are clicky, but the actuation is springy, which lets you roll it around smoothly, not unlike a tiny Sega Saturn D-pad or Neo Geo Pocket stick.
It seems the secret lies in Sony's perfect tolerances between the SMD metal dome switches, the silicone membrane on top of them, the plastic D-pad, and the shell itself. The pivot point in the center is the perfect size and height to prevent more than two neighboring directions from ever being pressed simultaneously.
GPD, Retroid, Ayn, and others have tried really hard to copy the Vita D-pad, but they've never perfectly replicated these super tight tolerances. On the GPD Win 4, you can push on the entire D-pad and press all four directions at the same time. That's physically impossible on the Vita 2000, so they really messed up the pivot point!
In Super Metroid, walljumping requires alternating left and right presses. If you ever press up or down during a walljump, you instantly drop the spinjump and fall. So the Vita 2000's ability to prevent spurious inputs is simply magical in that scenario. My other stress test is Level 8 of NES Battletoads. If you hold down to crouch and then double-click left or right, you'll slide on the ground. This is next to impossible to do in a controlled manner on less precise D-pads, but the Vita 2000 makes it trivial.
TL;DR: if you care about precision, focus on the pivot point. Having a nice D-pad makes Virtual Console and emulation way more enjoyable, so I hope you can figure out a good solution for your portable!