People seem to be asking three different questions: who was their favourite manager, who had the best team, and who made the most of what he had and improved the team available. The first two are easy, Jol and Redknapp.
The last, which is what the question asks, is more difficult. We know the results 'Arry achieved in the league, we know how he improved a number of younger players, and got us over the hurdle of beating the top teams. Against that he didn't rotate effectively leading to late season slumps in the last two seasons and he disregarded the lesser competitions (the Doneskh games in particular still rankle). Under Jol we had a far weaker team, yet still almost overtook Arsenal in the league despite a wage bill less than half theirs. Jol got twice the points per million pounds spent on wages that Wenger did. Against Jol was an inability to win the big games. Both played an attractive style of football, both lacked full support from the club in the transfer market, both entertained the possibility of other jobs (Saudi Sportswashing Machine, England) while our manager, neither won a trophy. I think its possible to make a good case for either being better by emphasising different criteria. In the end I picked 'Arry because of the better performance in the bigger games. He did have the better players, but he also helped them become better players.