I have no idea why there's a consensus that Sobers is a greater all-rounder than Imran, and I'm a huge Sobers fan. Both literally did it all for their countries, but from opposite ends of the bowling/batting spectrum. I don't see how you could possibly compare the two. And if we're being fair, one would end up with roughly half the criteria / disciplines having an advantage. For me the captaincy / fielding would balance each other out.
I would like to have a conversation with regards to this without the normal accusations.
One could say
Batting - Sobers
Bowling - Imran
Fielding - Sobers
Captaincy - Imran
But that solves nothing and is a lazy way out.
Primary skill
Everyone's ranking will be different but for me. Sobers is my 3rd ranked batsman of all time and definitely in the tier of best after Bradman. I have Imran ranked as 6th best pacer (and somewhere between 6th and 8th overall including the spinners) ever, and just outside of my top tier of bowlers. Only one is also able to walk into an all time team based on their primary skill alone.
Sobers for me here..
Secondary skill
I don't believe either was that great here to be honest. Imran was a below average batsman, but a very good lower order batsman. Sobers was likewise a below average bowler, but probably the best 5th option to have played the game. One edge to Sobers was that he could bowl fast, swinging fast medium, spin and chinamen, he also was called to fill every role from opening the bowling to being the stock bowler. Imran also went as high up as 6, though mainly (from memory) later in his career. Finally, of Imran's 7 hundreds none were game winning, infact only one came in a winning effort and none in the 4th innings. Sobers, though not much better had 3 (or 4) match winning 5 wicket hauls. Between the versatility and more match winning efforts I give this one to
Sobers as well.
Tertiary skill
It can be argued that Sobers was the best close fielder / catcher ever. He was in that absolute upper echelon on slip fielders with the likes of Hammond, Simpson, Waugh, Hooper, Chappell etc. he was equally brilliant at leg slip and short to Gibbs. It's often said Imran was a great leader of men and that certainly was one of the 3 pillars of what makes a great captain. Ability to lead and inspire, the others being win / loss record and being great tactically. I believe his w/l record would have been more than decent especially considering that he competed credibly against the best team of the era. Tactically he wasn't quite in the elite class, and while he instilled discipline, the team was hardly world class in the field. Think everyone would agree that captaincy is harder to quantify while being quite subjective and from what I have read from Smali over the years, Javed would have been the primary tactician. While both were respectively revered, taking everything into account I have to go
Sobers.
Intangibles
First the positives, Both were match winners, both were icons and respected by all. They are universally regarded as the best bowling and batting all rounders respectively.
With regards to the negatives. Sobers played in the professional era, but wasn't nearly as professional as he should have been. With modern disciple and focus God knows what he could have been without the partying and other liberties. He also captained himself poorly as a bowler and added to his own workload. As much as it's deflected, Imran had the shroud of tampering to deal with, and by his own admission was tired of the allegations of beneficial home umpires, but he also was instrumental to the development and advancement of Pakistan cricket and was noted as a mentor to the 2 W's.
Summary
They were both champions, and brilliant in their primary roles. Sobers however was a unanimous choice to the Cricinfo all time team and behind only Bradman with regards to voted for cricketers of the century. And we're not taking 15 or 20 votes in a odd voting system where biases can be felt. He got 90 of 100 votes. As great as both were, and they were superb, there isn't much of a doubt who the greatest all rounder was, as was supported by Bradman himself and echoed by the likes of Miller, Chappell etc.