You will find two general temperatures for non-colored LEDs, WARM and BRIGHT/COOL white. Then between manufacturers and sometimes production runs, there will be variations within those two main temps.
Which looks "better" is in the eye of the beholder really. But I'll go out on a limb here and say that universally "best" is determined by application and subject matter. One size does not fit all unless you are doing a sort of police line-up style display with no backgrounds or layout.
IDEALLY: Warm will give you something closer to traditional incandescent lighting, while bright/cool is supposed to be like a crisp high-noon sun on a winter day. In my experience, due to variation, bright/cool is not quite "daylight" - YMMV. I use warm for most of my displays and mix bright/cool with warm for my Hoth diorama. Many of my pieces are vintage and look more nostalgic under warm lighting, plus I'm also trying to match certain on-sceen looks/atmospheres in some displays which call for warm lighting.