Well, I didn't explain why I picked the PlayStation Dual Shock last time (over the 5200 controller), so I'll explain why I'm picking it this time over both the Dreamcast and Saturn analog pads.
1. I love the dual analog thumbsticks. They feel good, you can click them in for a third button, and they're in a symmetrical arrangement.
2. It's smaller than the Dreamcast and Saturn analog pads, but still big enough to be held comfortably in the hand. The DC/Saturn pads seem too big, considering they offer less functionality.
3. The digital pad on the Dual Shock rules over the DC digital pad any day of the week. The Saturn analog controller has a better digital pad than the Dual Shock, though.
4. The built-in vibration in the Dual Shock beats any of the add-on vibration packs I've tried for DC (which seem to weigh down the top of the controller, yet provide less "rumble" effect), and clearly beats no vibration at all on the Saturn controllers.
5. It offers the best balance of comfort and functionality ever. I don't have to say "this is the controller to get if you like racing games" or "this is the fighting game controller." The Dual Shock does it all, and does it all respectably well. I'm sure you can find better controllers for racing or flying or fighting games, but they all come up deficient in some other way. This controller has got it pegged.
I like the slots on the DC controller for VMU and other functions. However, much like what I said for the numeric keypad on the Jaguar controller, the usefulness seems to vary wildly. A few games make great use of the added functionality, but most make only nominal use of them. Few games use the VMU screen for anything but putting the title of the game or a cute little icon, and even fewer have anything that's useful in the heat of battle. It's better than nothing (which is what you get with the Dual Shock), but not enough to sway favorability on this one.
I also disagree with kisrael on the controller port issue, as it probably should come into play here since we're rating controllers and not the consoles themselves.

I think four ports is only a worthwhile advantage over two if the system actually comes packaged with four controllers. Most systems these days only come with one, so you're on equal ground, since you have to buy all the other controllers separately anyway. Now that we're talking about buying out-of-the-box add-ons, Sony actually wins, since one multitap gives you the potential to plug in
five controllers (not just four), and two multitaps give you the potential to plug in
eight controllers. If anything, 3DO (which wasn't even entered in this contest) would've smoked this category--the system only had
one controller port, but the controllers were daisy-chainable, so you could connect up to eight controllers without having to buy a multitap. I despised most of the 3DO controllers that have ever been brought to market (most of them were poor in design and/or quality), and I didn't like the system itself very much either...but that's one aspect that they really nailed perfectly, and it's a shame no one else has ever mimicked that feature.
I also feel that some people here are drinkin' the Haterade with regard to Sony, but there's not much I can do about that.
I think I've said enough for now.

Chalk up my vote for Sony's Dual Shock.