Availability and price - On this subject, the d6 is the undisputed king. You can find handfuls of d6s anywhere, usually cheap (or free, if you reuse dice from other games), and you can choose any color and size you like, in the farthest countries and in the nearest places (such as supermarkets), while d20s can be rare or expensive where you live, and hard to find in a hurry.
Nowadays, this isn't a big deal for most people, since you can order a d20 online for a couple of dollars or less, at least in most of America and Europe. Besides, RPGs are such a niche hobby that it is difficult to imagine that you play D&D and don't have a few d20s already. But there is no denying that d6s are easier to come by, specially if you are unprepared.
Abstraction - This isn't a problem with the d20, but of using a single die. When you have multiple dice, you can assign different meanings for each one (here you can find some cool ideas). There is also a characteristic of tangibility to dice pools that I love - you can physically “pick” successes from the table, move dice around (a GM might give special dice for certain circumstances or use dice of different colors), split dice pools, hoard and spend dice without the need to write anything down, and so on.
Although I really like this trait of dice pools and I have a house rule to use it in my D&D games, I can't find an elegant solution for people who prefer to use a single dice other than assign special meaning to each number on the d20, which, IMO, is less satisfying.
Granularity - In my latest post, I've said I like the granularity of the d20, in 5% increases. But you might prefer a d100, for more granularity - nowadays, I have a hard time imagining that someone would enjoy distinguishing a 92% to a 93% chance of falling, but I did in the past, and I still like plenty of d100 systems. You may also think a chance smaller than 5% would be useful for specific situations - say, 1% chance of any given stab-wound causing immediate death. You cannot do such thing with a d20 with rolling multiple times, using "exploding dice" or "confirming criticals".
On the other hand, you may think a 5% difference isn't relevant enough, and prefer to use a single d6 or a d10, to stay within the proverbial Magical Number Seven, Plus or Minus Two. If you don't like this level of granularity, you'll probably also dislike the tendency for near-irrelevant +1 bonuses that many D&D games use for traits, magic weapons, feats, etc.
I don't think too much granularity is a problem, unless you take it as a justification to count every +1 bonus you can find. In my own games, I use the d20 but usually avoid +1 bonuses (I use +2/+4/+10 most of the time). In any case, this is mostly a matter of personal preference.
|Sometimes, the dice aren't on your side.|
“Swingyness” and the bell curve - Some people say that you have the same chance of rolling 12 and 15 on a d20, while it would make more sense if a 15 was harder to come by, and the results were spread in a bell curve.
Contrary to many, I do NOT think that this is a problem of the d20.
The problem with this idea is that it assumes there is a DIFFERENCE between rolling 12 and rolling 15, which is not always the case. Let us say, for example, that you have to roll 11 or more to succeed in a task. Whether you're rolling 1d20 or 3d6, the odds are always 50%. Likewise, if you want a character to have a 10% chance of success, just say she needs a to roll 19 or 20 with a d20, or 15 or more in 3d6.
3d6 does NOT generate a bell curve if there are only three or four possible outcomes (pass, fail and crit). Think of it this way: if you were creating a graph for such results, you wouldn't have 16 points (the numbers from 3 to 18) to create a bell curve, but only three or four (success, failure, crit, fumble), exactly as you would with a d20.
Maybe if you're working with margins of success, and want they to vary little, this may become a bit of a problem - but D&D usually doesn't.
Still, there are some situations in which the lack of a bell curve can cause real problems, including what happens when you compare different characters. The subject deserves an extended analysis, which is why we'll cover it in the next post.