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Short answer: there's no real difference between the two types.
The type of dice you're calling crystal are also known as rolling-pin or rolling-log style dice. They're actually just n-sided prisms with the ends tapered so they never land on them. Rolling a prism die like this is just as fair as any other die.
To see why, take a look at a picture of a prism -- Wikipedia's article on pentagonal prisms, for example.
In that article, there's an image of a 5-sided prism at the upper right. A die in this shape would have 5 rectangular sides around it, and 2 pentagonal ends. If the ends are convex enough (like the "crystal" dice of your example link), then the die can never land on them. This leaves only the 5 rectangular sides as options. All of them are evenly distributed around the "waist" of the die, and all of equal size. Therefore, they're all just as likely of landing points.
Do note that the density and symmetry problem can show up on both kinds of dice. Just because they can't land on some ends doesn't mean they're good dice.
There are several key advantages to barrel shaped dice:
I find that I like them well enough when used with a dice cup. But when not used with a dice cup, I don't much like them.
Besides, there are other shapes of dice besides the "normal" ones that ARE fair, but sure don't look it... the Gamescience d7 is fair when used with dice towers and/or dice cups, but can easily be thrown for a flat by hand on tables with a tablecloth.
Because of the nature of the fact the rolling-dice can only roll in two directions (forward an backward), whereas a standard dice "tumbles" in any direction, it may be easier to modify the dice by filing a particular edge so it's wider than others...
I'm not talking from personal experience, as I have only recently started playing table-top RPGs and haven't seen one of these die before, but I'm thinking in practical terms.