I don't know that anyone can approach this question without some degree of bias. A lot of points can be made in both men's favor (and some made here already are ridiculous).
I think another thing that plays a major role is the fact that Bryant was not just a Tide coach, he was also a Tide PLAYER, a man who met his wife on campus in the 1930s. Saban is not - in that sense - 'one of us' and I think this colors the argument for some people. Another thing is the whole 'adoring the unseen.' Let's face it - if you're my age (46), you BARELY remember Coach Bryant, whom I caught on the tail end of his career (the 1978-79 championships).
Let's get rid of a few of the more ridiculous arguments here. Trying to argue Coach Bryant should have had more titles borders on the absurd at one level. You can't have it both ways. The same fans who tout 1964 and 1973 by saying "that's just the way it was then" try to jigger the outcome for 1950, 1966, and 1977. While it's true Alabama sort of 'got hosed' in 1966, the Tide benefited in 1965 from a one-year change to the rules caused by the 1964 outcome.
Saban may not have won ten games in a year consecutively prior to 2010, but he also never went to eight straight bowls and came home winless, either. (If we're going to make those kinds of arguments......) And let's just set aside the notion Saban CREATED the monster that won those games....
Here's another one that begs for context:
Imagine CNS dealing with segregation, the image of southern people as inferior and having the majority of sports writers from regions that hate southern football.
This is hilarious in light of the fact that a simple perusal of this board shows that folks here think the last two points (especially the LAST one) are constant problems nowadays. I think Saban would deal with segregation pretty much the same way and has the same advantage Bryant did in being from what is essentially a Southern state. That Southern upbringing with Bryant was a major advantage (particularly his being poor) that helped him relate.
Bryant didn't have scholarship limitations or coach in the SEC during its most competitive era. Now this has the potential to be overstated. Bryant came to Alabama in 1958 and consider the fact that LSU, Auburn, and Ole Miss all won national titles along with Alabama in the 1957-1961 time frame. But for the rest of his tenure, the SEC wasn't really all that big a deal. In EIGHT of the seasons between 1964 and 1982 (19 seasons), there was only ONE OTHER SEC team ranked in what was then a Top TWENTY (not 25). In three of those eight years, that team didn't even play Alabama and thus you might have even fewer ranked had those teams had another loss. Saban, on the other hand, has competed against teams from LSU, Florida, and Auburn who won it all around the Tide's titles in addition to facing an Auburn team that came within twelve seconds of winning it all and another national champion that beat us head-to-head in a semi-final. Keep in mind Saban also faced a top-ranked Mississippi State team in 2014.
It's true that Bryant did not have the modern recruiting advantage, but I would argue he had something better: the name (Alabama) and the fact that back then teams did not play on TV more than three times a year. Florida as a state did not have three competitive teams so he was snagging talent from there.
Of course - as with everything - there's also a flip side. Bryant had two undefeated national champions (Saban one) and a third unbeaten team (1966). We can argue over who had the tougher job to inherit - Alabama had won four games in three years when Bryant was hired but the team had been in a dumpster for eight of the previous ten years and was on a second probation when Saban arrived. Bryant's players played both offense and defense rather often (it was expected back then) and with inferior equipment and training methods compared to now.
Both guys inherited dumpster fires and turned them around. Bryant won an SEC title at Kentucky ("Marty, I just got back from 2015 and UK still hasn't won the SEC since 1950!") and a SWC title at ATM; Saban won national championships at TWO schools in the toughest conference.
Both guys had some extraordinary luck winning national titles - Bryant with the AP's fortuitous decision to wait until after the bowl games to select a champion in 1965 (along with the two titles that ended with losses) and Saban benefiting from the bizarre computer gimmicks of the 2003 BCS (while he should have been in the game and OU should not have, LSU only made it because Boise State beat Hawaii and Syracuse throttled Notre Dame - those two losses crippled USC's strength of schedule) and Ohio State being on probation in 2012.
One thing I would point out is that across ALL sports the quality of play and competition has improved greatly. Baseball had 27 times where a guy hit .400 or better from 1876-1941, a period of 65 years......in the 75 years since it has NEVER happened. Do any of you REALLY think that ALL of the best hitters to ever play MLB played in ONE era? Of course not. Cy Young won 511 games.......and ALL of the top six winners in baseball history played more than 50 years ago.
Again - do ANY of you REALLY think that the best six pitchers of all-time pitched prior to 1965?
Me, neither. I'll have more to say later, worship beckons me.