From what I found in a quick Google search, those are two different print developers. Eukabrom is a normal, neutral tone formula, and Centrabrom is a soft contrast developer.
Ansel Adams used to use Dektol (equivalent to Eukobrom) and Selectol Soft (roughly like Centrabrom), along with a water bath, to control contrast in graded papers before variable contrast papers became available. He'd determine what contrast he needed via experience and test strips, then if he needed to print "between grades" he'd print on the next harder grade and use Selectol Soft to soften the contrast by a half grade or so, move the print from Dektol to Selectol, sometimes with some time in the water bath between or after.
Normally, today, you wouldn't need to do that; if you have variable contrast paper, you can just select the correct contrast filter or color setting; if necessary, you can "split filter" by printing the highlights with a 0 or 00 contrast filter, and then print the shadows with a 4 or 5 filter (for a color head, 0 would be yellow light, and 5 would be blue = magenta plus cyan). There will always be some printers who will insist they get a better quality of some kind by switching up the developer (using a soft developer for certain images, and a harder one for others), but you have to decide what you need for your prints. For myself, split filter printing and one developer (Dektol equivalent, like your Eukobrom) will do everything I need to do with black and white variable contrast (aka multigrade) paper.
