Gochugaru powder vs paste?

If you are referring to gochujang, gochugaru and gochujang have significantly different flavors (gochugaru is thought to impart a "cleaner" hotness to dishes, while gochujang tends to be a bit more complex due to aspects like added sugar and grain e.g. rice flour (which adds a thickening element) and some fermentation.

Thus Korean recipes will often use both, and as a rule of thumb gochugaru is the more flexible of the two (due to being mainly used for only hotness and color). In addition, while gochujang is reasonably replaceable with gochugaru + some sweeteners and thickeners, trying to replace gochugaru with gochujang is generally a bad idea. I'd recommend trying a different kind of relatively fine red pepper flakes - preferably a less spicy and less "aromatic" (i.e. one that has few flavors and aromas outside of "hot") variety, although your mileage may very depending on the type your local market has.