I've collected a few different things over the course of my life. Very old cameras, vending machines, electric fans 1940's and older, and now cast iron cookware.
Cameras, some people collect brands, but a lot more collect certain types of cameras. Rangefinder cameras, box cameras, folding "Pocket" cameras, press cameras, etc.
Vending machines, people do collect certain brands, but it's not as common as collecting what you like.
Antique electric fans, kind of all over the place. Personally I would pick up what I liked, but gravitated towards one brand (Emerson Electric) because of the quality and ease of repair. The rest were just filler. When I was into it, it seemed like most people just wanted 1 of every type/brand of fan.
Cast Iron cookware, I personally just pick up what I like, I've slowly gravitated to two brands, neither is Griswold or Wagner. I've only got a few pieces of each of these brands, but my goal as a collector is now to build a set from each of "MY" brands.
I think the appeal of Griswold is the LARGE logo, the nice clear lettering, and the quality. I can't help but think that if Wagner had made their logo larger, etc etc... They would be even with Griswold. There's a reason why People pay $30 - $40 for a No. X, un-marked Griswold made Iron Mountain skillet, but will pay 3-5x that amount if it has a nice large Griswold logo. Same quality. Marked goes for $$$ Same goes for Victor, look at the pieces that are just marked Victor, -vs- the pieces marked Victor, The Griswold Mfg. Co.
With something like cookware, I'm sure sentimental value comes into play as well. Grandma had Wagner, so it must be the best. Mom had Griswold so I should buy that, etc etc... Fact is, there are a number of companies that met, and exceeded the quality of both, but didn't have the marketing muscle to become household names.
</rambling>