With respect to game controllers, I have seen two main styles of directional pads, and I want to know which type is generally considered the best.

1. Nintendo style, with just the four directions. For diagonal inputs, you need to press two of the directions at once.
2. Sega style, with the rounded circle, where diagonals are part of the pad itself. (It looks like Sega abandoned this design for the Dreamcast, but the Xbox 360 controller uses it.)
(There's also the Sony approach of splitting the directions into separate buttons, but I've never heard people praise the directional controls.)

So, which of these d-pad styles is considered best?

Best D-pad is the one you don't need to use, or only for quickslots and switching between modes. ;P

I find movement with D-pad very uncomfortable and much prefer the analog thumbsticks nowadays. D-pad tends to give me blisters.

Well, you could test this by trying to press left and right at the same time.

Interestingly enough, some games behave strangely; in Zelda 2, for example, you can accelerate so quickly that is is not reasonable to control it (outside of a TAS), and your velocity will constantly overflow and switch sides. The problem with analog sticks is that they don't work well for when the game has 8 directional movements, and where the wrong movement could prove fatal.

In a game like Celeste, for example, you can dash in 8 directions (including diagonal), and accidentally dashing in the wrong direction is a likely cause of death.

Another example would be roguelikes, though many console roguelikes (and even some computer ones) have adopted the convention that, if you are holding a certain button, only diagonal movement will be possible. (Tangledeep does this, for example, and I first remember encountering this with Mystery Dungeon games like Pokemon Resuce Team and Shiren the Wanderer.) Again, in a roguelike, a bad movement at a critical time could result in a death, and unlike Celeste, roguelikes tend to punish death harshly.

One thing is certain: The d-pad on the 360 controler is bad. It is *really* bad. You do not want to use that thing. Proper control with that thing is impossible since it does not have anything like a pressure point, you do not really notice if you have pressed a direction or not. It is also wobbly and has the tendency to hit down when you try going left or right.

The d-pad on the Xbox One controller on the other hand is way better. It has a very defined pressure point. In my opinion it is better than the d-pad of the Nintendo Switch pro controller.
That one, and the d-pad of the SNES classic controller are ok.

I cannot say anything about sega consoles, I have played a Megadrive (aka Sega Genesis) maybe two times in my life, and never any other sega consoles. Same for Playstation.

While I liked the Mega Drive d-pad much more than the Famicom or Super Famicom d-pads, my favourite d-pads were the NES Max "cycloid" and one on a third party gamepad made by a company called Alps for the PlayStation. The 360 d-pad is one of the worst I have ever used.

And yes, the Sony d-pad is a single piece of plastic, not individual buttons.

The x360 d-pad is indeed terrible, but the X-Box One dpad has been fine for me. It also produces satisfying clicks. I'm not sure how common this is.

I can't remember the "Sega style" since I don't use a Sega controller more than a decade ago.
However the implementation on each design is more important than the style itself.
That said, stay well away from the xbox 360 d-pad. Even on menus is not uncommon to choose the wrong slot...The Xbox one seem fine but with separate individual buttons maybe some training needed to pull half-circle tricks like Ryu's circle kick or some Mortal Kombat fatalities (or many Tekken moves).

The PS style is fine on better quality controllers as is the Switch style.

I've recently got the 8bitdo sn30 pro+ and is hands down the best overall controller I ever had. Works ony any machine I could test (Windows, Raspberry and Android), wired and bluethooth. D-pad very good as are the analog joysticks and triggers. Have between 50 to 100 hours on it ranging from d-pad fighting games to analog/triggers racing-sim games, not a single issue so far. It's also very affordable.

Just something I noted, on Windows bluetooth devices (be it the controller or a speaker) can cause lag/stutter and wifi interference. Usually a reboot fixes the issue.

Edit: the cable included on the 8bitdo controller is short, probaby little more than 50cm and is USB type-c wich is way much firm and reliable than micro-USB, wich tend to loose connection or disconnect too easily.