With Roblox’s new beta character controller announced, I’ve returned to say that as of now, I still think PhysicsCharacterController, even with its lack of swimming and climbing noted in the first post, is better than it for satisfyingly smooth movement. 
This video shows how smoothly I can curve around obstacles, which I can’t do with Roblox’s official physics-based movement (as it slows me down any time I change directions, unlike here, where turns smoothly transfer momentum).
My settings for PhysicsCharacterController
- Bounce: 15
- FlatFriction: 150
- HipHeight: 3.306 (edited calculation in scripts somewhere for better foot alignment)
- JumpDebounceTime: 0.175
- JumpPower: 425
- Suspension: 1000
- WalkSpeed: 45.25
- XZDragFactorVSquared: 0.177
In case this isn’t worthy of a reply to this topic, I have a bug to report; If your game or Roblox Studio lags for any reason, the physics completely break, usually making my character bounce very high into the air, becoming impossible to recover from if enough lag happens.
If merely moving your mouse cursor around the 3D viewport makes Studio lag like my computer unfortunately does, try shaking it around constantly and as the framerate stays low, your character may go flying… This reminds me of a very iffy game engine named CopperCube, where the framerate dropping also made physics unstable. When someone tried my baseplate, I guess they had a really bad frame rate, as they bounced like this constantly while I had PhysicsCharacterController on.