The 'Dual Shock' has to be one of the most overrated things in video games ever. The whole layout of it is archaic due to the fact it gives precedence to the d-pad. We all know that control sticks are better for 3D games whereas d-pads are better for 2D games, but ever since the N64 and Playstation came along 3D games have been by far the norm, therefore any game controller should be more catered to 3D games. Nintendo, Sega and Microsoft realised this which is why the controllers for the Gamecube, Dreamcast and Xboxs put the control stick at the top of the controller and the d-pad below and why those controllers are superior to the Dual Shock. Sony should also have realised this and should have switched the d-pad with the control stick at some point.
Every time I play a PsOne game, I will always use the d-pad if I have the option to. Not too long ago I played through Spyro 1 and 2, I tried using the control stick, but I found it was far too awkward stretching my thumb down the controller towards it. I rarely play a PS2 or 3 due to not owning one myself, but I when I do I instinctively try using the d-pad because it's where the control stick should be, and then I stink at the game since I find using the stick completely 'wrong' - awkward, uncomfortable, unnatural etc. It's not just the Dual Shock, the Wii Classic Controller has the same design and ergo the same problem - it's great for playing 2D games (which I guess it's primarily designed for due to the Virtual Console) but I hate trying to use it for games that require you to use control stick such as Brawl or N64 games.
There's not much else wrong with the Dual Shock, and if it wasn't for that flaw it probably would be perfect. However that flaw is a massive flaw which makes it a poor controller in my opinion. The popularity of it has always completely baffled me.
The best controller ever in my opinion is the Gamecube. It's the Dual Shock done right, along with a few extra great things. The control sticks are amazingly comfortable and responsive (and in the right places); the face button layout works well, I find it easier to move between those 4 buttons than I do the conventional + layout; the triggers are excellent, extremely comfortable and responsive, and the pressure sensitivity works really well for games like Super Mario Sunshine; it's nice to look at; it's very comfortable to hold and use... It's as close to perfect as we've had so far, the only reel fault it has is the small d-pad.