The 5th does nothing to define the "color" of the chord. It reinforces the fundamental but does nothing to denote Maj/Min. It provides added power, and strength to a chord, but with no 3rd, you have no key tonality. The Root, 3rd and 7th define the nature of a chord. The added "color" tones (2nds, 4ths, 6ths) provide more detail, and tension. In practice the Root and 5th work together to reinforce the overall tonality that is defined by the 3rd and 7th.

I wouldn't say that it's a case of more, or less important, as much as it is not as necessary in naming or defining a chord. Take organ stops as an example - the first 3 drawbars are 1-5-1, and used together, they sound like a solid tonic.