I've never bought into the binary thing when it comes to entertainers. I like both singers. IMO, they have very different voices so the David Cover-Version cracks never made much sense.
I suspect Coverdale has had to work harder than Plant in order to sustain his career. He probably has made more artistic compromises along the way. Plant was THE VOICE OF LED ZEPPELIN. He was in one of the most successful bands of all time and considered one of the best rock singers of his era. By the time Led Zeppelin folded, he had achieved iconic status. Coverdale, in contrast, was Deep Purple's third lead singer. He was considered a fine singer, but not the one most fans associate with Deep Purple. That honor goes to Ian Gillan.