Since the very start of my dalliance with coffee, caffeine content has been the one question that comes up most consistently. It's also the question whose answer has changed the most frequently in that same span of time. "We" keep learning new things - here's where we're at now.
It doesn't really matter.
Kind of a boring answer, yeah? Probably why all the myths are more fun to share.
However, the details are more interesting. Dark roasts contain more caffeine as a percentage of the bean's total mass. Light roast contains more total caffeine. The difference in caffeine quantities between the two, however, are negligible - using slightly more or less coffee (a slightly higher heap on your scoop, the margin of error on your scale) has a far greater impact on caffeine quantities in your beverage than roast level selections.
For a long time, it was understood that dark roasts have less caffeine because it "cooks off" during roasting - this is both true and completely wrong, in the fun way that questions with detail-intense answers can be. Some caffeine is lost during the roasting process, but caffeine is stable at all typical roasting temperatures - even this study, that remorselessly over-roasted beans in the name of science, found only 5.4% of total caffeine lost during those most severe of conditions. The caffeine that is lost is mostly taken via the moisture loss - caffeine may be stable at those temperatures, but it is water soluble at all temperatures and some would be lost that way.
Some more interesting information, if you're particularly keen on your buzz ...
Caffeine is water soluble, as mentioned above, it's actually one of the most "accessible" compounds in your coffee, and will extract nearly completely almost immediately. Once your coffeemaker has been brewing for between 30 seconds and a minute, depending on your grind size, your pot has all the caffeine it's going to get. The taste will continue to change as it navigates your extraction profile, but the caffeine is fixed relatively early.
"low quality" coffees will often contain more caffeine than high-end ones. Most craft roasters don't use Robusta varieties outside of espresso blends because it's often not as tasty as Arabicas, but the Robusta beans do contain noticeably more coffee than their Arabica counterparts. Many low end producers will pad Arabica blends with less expensive (and more caffeinated!) Robusta beans. (We don't; we also don't use any in our espresso at the moment.)
It's genuinely pretty hard to measure caffeine content, and certainly not possible at home or your local cafe. From the study I linked above, the researchers needed to use "HPLC" or high-performance liquid chromatography to separate and measure each component of the solution. This is a pretty complex and very expensive (~$20,000+) machine, so there's not a commonplace practice to measure or check.