I thinks it's common sense that Klopp has been more successful than Rafa or Houlier. The main difference is the Premier league title. And let's face it, if it wasn't for the incredible city team, they'd have won 3 of those. Plus they reached 2 ucl finals.
Their "title" was during a period when football was the very last thing on people's minds, people at that time were seeing family members die, and being taken to hospital on a regular basis.
Football behind closed doors on a regular basis isn't football.
People back then were just happy to be alive, so thinking about a league title or whatnot didn't really register, and wasn't important.
So their "win" has to be put to one side, ot is simply impossible to put it in the same light or same category as every other league title that has been won by themselves, and other clubs.
So with thar in mind, a Klopp like Houiller am Rafa has won cups as the highlight of his time as Liverpool boss.
Rafa's Champions League win was against a very, very good AC Milan side, Klopp's against Spurs, so Rafa comes out on top there.
Houiller won 3 trophies in one season, including a European one, and we know how hard that is to do (we obviously surpassed it), so that success is something that Klopp has yet to match.
As for finishing second to City, Rafa finished above us under Sir Alex if I am remembering correctly, which is a vastly superior achievement to finishing second to City, as Sir Alex is a vastly superior manager to Pep.
So, no matter how you wish to look at things, Klopp is the third best Liverpool manager of modern times (Bob Paisley is obviously their best ever one).