While tinkering around in the simple system I'm yanking out of West End Games' Ghostbusters game, I pondered changing from using six-sided dice to using four-sided dice. I find the ubiquitous six-sider boring, though it's far more accessible to non-gamers who might be better able to pick up this rules-light system as opposed to the monstrosities that are latter-day editions of D&D. Four-siders are my favourite die, followed by twelve-siders, so I thought I'd look into how the game might change based on a different randomiser.
Adjusting the difficulty numbers assigned to tasks is simple: the standard range is 5 (easy) to 30 (difficult), with a new level after every five numbers. Well, I see that 5 is 6-1. Six is the maximum you can roll on one d6. So for every "level" of difficulty you should be rolling one more die if you hope to succeed. You would have a hard time rolling a 5 on a d6, but most characters don't have scores of 1 (I think 2 is the minimum, though injury or unusual circumstances can cause you to lose points in your traits), so we can safely assume the player will be rolling at least two dice. If I apply the 'max on die minus one' formula to the d4, I get a scale from 3-18. Again, it's hard to roll a 3 on a d4, but if you're rolling two of them, not too bad. So adjusting the scale of difficulty numbers seems to translate okay.
However, with only four possibilities whenever you roll a die, the Ghost or Skull Die becomes a much larger threat. The probability you will roll the skull and have Something Bad happen leaps from 1 in 6 to 1 in 4. That's significant. It could be justified by the setting -- if you run a dark horror or post-apocalyptic game with a deadly and/or scary mood, where the PCs should expect awfulness to be around each and every corner, it might actually benefit you. I don't know that that's a good idea for my setting idea, which I'm planning to be mostly serious but not grim, with ample opportunity for some comedy/foolishness/slapstick.
So the jury's still out on this one. I'm still very much in the brainstorming phase of the setting, and I'm assembling the rules (mostly, as I said, pulled right from the pages of the Ghostbusters book) bit by bit as I go, so there's plenty of time to tweak and experiment.