Broadly speaking, two things govern the stability of a basic inkjet colorant: the stability of the molecule itself and its environment, which includes not only the solvent, the receiver matrix, etc., but also the morphology, that is whether it is a more or less isolated molecule (dye-based colorants) or an agglomeration of molecules (like a pigment).
One may also ask "stable towards what?" More on that in a moment.
Given similar chemical structures, pigments are likely to have greater stability than the corresponding dyes. However, it is entirely possible to have a pigment made from an inherently low stability molecule that would result in a lower stability ink than a dye ink made from a high stability molecule.
That said, this is unlikely to happen as manufacturers choose the best molecular stability they can get subject to other attributes (color gamut, dry time, water resistance, etc.). So a good rule of thumb is that pigmented inks are likely to be more stable than dye-based inks.
But stable towards what? For a long time, one of the best known contract testing labs was testing only towards light stability, resulting in some truly embarrassing predictions when the product's ozone stability was simply awful, and prints faded from ozone exposure long before light could get them. (Even after this lab started to include ozone testing in its repertoire it coyly omitted ozone ratings with an eternal "Test in Progress" rating for its contract customers whose products did not do well in ozone tests.)
Other factors that are important are thermal stability (sometimes called dark stability, though it occurs in displayed pictures as well) and humidity resistance. The first company to insist that all four factors be tested was Eastman Kodak who had been doing such tests on its other imaging products for years (silver halide prints are not usually subject to ozone failure).
It's also important that all four factors be kept in balance if one wants to predict real world lifetime. Use too high an assumed light level (such 450 lux) with too low an assumed ozone level and you might predict that a displayed print with good light stability would last much longer than it really would, sucumbing first to ozone-induced fade.
So back to the dye-based ink that is supposed to last 200 years in albums and 100 years under glass, presumably with light exposure. Yes, it's possible. But unless the company is a well-known one whose image permanence lab is unlikely to publish bogus results, I'd ask to see both the data and the methods of testing. As a customer, you have every right to ask--nay, demand. (The large companies discuss their test methods both in their own literature and in papers given at conferences sponsored by the Society for Imaging Science and Technology.)
And when in doubt, pick pigmented inks from a well-known manufacturer when image permanence is a primary factor. Original manufacturer's inks may cost more (though at least one inkjet printer company is marketing its own pigmented inks with excellent stability at a price very competitive to off-brand inks), but you'll be glad you did for pictures you want to have last a lifetime.
