I think the measuring stick of a.) winning more games over b.) a longer period of time; demonstrates the better coach. Yes,... in other words the number of Championships as a contention for determining greatness is a faulty barometer. ( See Weeb discussion.. )
After-all what is it that a coach does. He pulls the best out of the players he has in any given year with the goal of winning it all and is hired to do so for as long as he can. With flash in the pan teams and even those that put together multiple years of winning its no wonder that even the winningest coach of all-time won't win any more championships than another great coach. Hence Shula's moderate Championship title resume.
However, coaching in 5 decades and of averaging close to a 70% winning record, 33 years of always being in the top 20% of the best teams year in and year out, proves to me that he could coach in different era's, different player mindsets (...ego's grew..etc.) different rules changes, different teams etc..... and yet still he won. Nyjunc is right in this regard: It not really debatable. It's Shula hands down
How do you take a 10 year record, as good as it is and measure it against a winning record of games and longevity over 3 times that snapshot of a career? Sure he may not have the number of championships, which just means that on any given year there was a better team perhaps. But, lets see what Lombardi would have done (as great as he was) if he had coached into the 80's against greater competition, ego-maniacs, WFL's and USFL's etc. softening rules and new fad pass happy schemes.