All CD-Rs store information as 1s and 0s. A bit is a bit, so CD-R brand does not matter. I have CD-R music discs from the 90s that still play as good as new; all of them different brands. Take care of your discs is my best advice.
Taking good care of your disks is sound advice. But, like bomberboysk said, the type of dyes used in the CD-R will make a difference.
The old rule of thumb was: Green CD-Rs are the cheapest and have the worst durability. Blue/Gold is the more expensive, longer lasting type. All CD-R media use either gold or silver as the reflective coating one of three dye polymer types as the actual recording medium. Stamped, commercially manufactured CDs use Aluminum and have no dye. This still pretty much applies today.
Cyanine is the cheapest, least durable form of dye used. This is a light blue dye that will show up as a light green color with a gold reflective layer or light blue/green with a silver reflective layer. This is the original "Orange Book" (recordable CD media) spec'd dye that used to have a shelf life of about 10-20 years and through recent formula changes (metal stabilized) has a claimed lifespan of roughly 20-50 years. Over time this dye will tend to be affected by ambient light (particularly UV) more than others. It also offers the lowest reflectivity contrast that can lead to read errors.
Phthalocyanine is a nearly transparent dye that is more stable than the standard Cyanine dye. This is most commonly used with a gold reflective layer producing a gold colored appearance. This combination offers the best reflectivity quotient and longer data retention due to chemical stability. Phthalocyanine based disks claim a data retention shelf life (under ideal conditions) of about 100 years.
The more recently developed
AZO or Metalized AZO dye was developed several years ago by Mitsubishi. Most Verbatim disks today use this formula. The AZO dye is a dark blue dye typically used with a silver reflective layer. This results in a dark blue recording surface. Manufacturers claim this formula to be on par with Phthalocyanine "gold" disks for data retention and longevity.
Since recording media hasn't been around for more than a couple decades yet, the claims for either media type cannot be truly verified. Different brands DO use different types of dyes/substrates as I mentioned above. It DOES make a difference. I hope this has cleared up a few items. Let me know if you have any further questions.