Natural black hair is, in my opinion the best especially if you have white skin (british for example), look at actresses/famous woman with natural black hair (eg: daisy lowe, katie mcgrath). I find it being the most attractive because it creates a great contrast especially with green, blue or light colored eyes, but it looks amazing even with black or brown.
Natural red is the second on my list ... here I'll give you examples like Karen Gillan, Isla Fisher, Julianne Moore ... this however looks best and even though I may bee harsh, only on very light skin, freckled woman. I personally have no objection towards "gingers" as someone above me underlined, I find them interesting and intriguing.
However, dyed black hair I find to be tasteless especially if it doesn't fit your complexion (eg: Cameron Diaz, Miley Cyrus, Lily Cole), because it doesn't look good any everyone and to get it done poorly is another big mistake. As for red ... this is very tricky to get as well for the same reasons as for black. Not all people can wear it properly and it might end up being a bad decision afterwards.
I personally am brunette, dark brown, and have been thinking about dyeing it either balck or red to be honest. I have light complexion and freckles ... lol ... I know. But after I saw an old classmate on mine, who has beautiful back hair, having dyed it black ... stupid in my opinion, seeing as it was clear that it was dyed and also, her natural color looked infinitely better than the dyed one. I decided against it because I like my hair color and there are also other things than the ones mentioned above: For black ... it makes you look older if it's dyed ... and not in a good way.
So whichever was the reason for questioning about black and red hair, just know that natural it's the best course of action.