I agree and I am quite enjoying this discussion.
Medhavi - I feel you are making a few generalizations in your earlier post. Cases in point are:
- Rafi was better at Rock and Jazz music
Now, Hindi film music - even for that period - was not what you would call Rock music. There were a few examples though. One of them is the unforgettable 'Mere Umar Ke Naujawanon' sung by Kishore. Now, that is a rock classic in the truest sense of the word - at least as far as Hindi filmdom goes. 'Pag Ghunghroo Baandh' can also be extrapolated into the 'Rock' genre if you are not too picky

.
I cannot seem to recall many popular Rock songs sung by Rafi. Jazz on the other hand, Rafi has sung and sung well. Now, whether he sang it better than Kishore - that is subjective, unless they both sang the same song.
And that, luckily for us, happened. As you rightly point out, 'Tum Bin Jaaoon Kahaan' was sung by both the legends. And there are no points for guessing whose version was better and whose version became popular. Yes, Kishore sung the song far far better than Rafi did. Lest this be a subjective opinion, I encourage members to listen to both versions and make their own decision.
Next up - Rafi was better than Kishore on sad songs
The pathos that Kishore could bring was not restricted to voice. It extended to its timbre, expression and pitch. Can you imagine somebody singing 'Yeh Laal Rang' with a smile on the lips? Yes, if you listen to the song, it is one sung with the utmost sadness of spirit but with a smiling mouth. That is genius. Or lets take 'Yeh Kya Hua'. Now, thats again such a distinctive sad song that it begs mention. It falls into a distinct genre actually. It had that maudlin quality. It was rueful, but gently rueful - not bursting into sobs. These are just two examples.
If you get into true pathos, songs such as 'Kiska Rasta Dekhe', 'Koi Hota Jisko', 'Koi Humdum Na Rahaa' etc. are true gems. I am also a die hard fan of the song 'Jin Raaton Ki Bhor Nahin'. I consider that a very high example of Kishore's emotive skills with the microphone. It was also an example of excellent composition. Which reminds me to mention that I am only talking about Kishore the singer all the time. If we bring in his other dimensions, very few people in the history of Indian cinema can stand the comparison
Next up - Rafi is better than Kishore in fun songs
Now, that really is something I dont comprehend. Like I said, Kishore and fun sort of went together. He could take an ordinary song and infuse life and an inimitable dance quality to it. Examples are too many to list here. In this more than anything else, the difference between Kishore and Rafi is much too apparent. And we need not even go to his yodelling skills to sort out the winner here.
What I will wholeheartedly agree with you on is that Rafi was the better Qawwali singer. And of course he was the better classical singer. But if its versatility as a singer that we are looking for - a man who could go high or low, skim on the surface or go deep, scream or whisper (Oh Meri Sharmilee) - then it is Kishore who comes on top.
Personally I love the sad songs sung by Mukesh and rate them at par with ones sung by Kishore. But if there is a comparison, it is again the versatility aspect that places Mukesh at second spot.
Consider this, if you will. If I come back from office all 7 days of a week in a different mood, there is every chance that I will be able to select and hear a song matching my mood perfectly sung by Kishore. And what is more, revel in it. Now, that is a very difficult thing to have done as a singer. And I appreciate it. I dont think I can say the same thing about too many of the Hindi singers at that time. But as they say, each to his own.