It's a different color, I consider it purple, my favorite part of the color spectrum. Purple can be made with both blue and red, but still is a completely different color. How would you consider water? Like liquid oxygen or wet hydrogen? Or just like water?
Colors are very dependent on cultural context so if people would put their countries along with answers it'd be nice.
I personally think it's completely separate and not really comparable even though directly translated from Icelandic the color is "violet blue". From Iceland
Erm what?... That's a pretty bizarre question. Like asking if a fork is more of a spoon, or a butter knife. Purple is not a red or a blue, it's a mix of red and blue, not a discrete wavelength. Violet and indigo may look similar to it but, unlike purple, are discrete wavelengths.
If one has to answer the question, it depends on the red and blue used to make the purple.
I consider it a cool color because I can usually wear it and look good, and generally cannot look good in warm colors. But never thought of it as a red or a blue just purple.