I can only speak for myself on that matter, since I would say Trapattoni is quite a polarizing coach, which means that there might exist 5 opinions about him among 3 different people. Here's my two opinions:
First off I rate Trapattoni as a person and as well as a coach, I always did. His reputation did as we know not come out of the blue, but due to a lot of success he has had as headcoach of Juventus for many years, FC Internazionale (helping them to clinch their last national championship title in 1989) and FC Bayern Munich for example.
I do not, in contrary, rate his way of letting his teams play football (the 4:3 against Maritimo last week being the exception here, I never seen a Trapattoni-managed side play like this before): very defensive, very focused on the result, not on the game itself. Benfica for me stands for offensive football, a spectacle. Trapattoni's style in my opinion fits to italian football, but not really to Benfica though. That was my thoughts at the beginning of the season, but partly, I must admit, Trapattoni proved me wrong. It's not that he proves me wrong in my suggestion of how Benfica would play under his reign, but in my suggestion of how effective this might be. We are at the moment facing a hughe euphoria, being as near to the championship as we have not been in a long time, plus we have good chances to probably raise the portuguese cup as well this year. We are not outplaying our opponents week in week out actually, as one possible reason for our temporary domestic success, but we play very efficiently, at least over the past few weeks. When we can make profit out of a situation, like Porto and Sporting losing for example, we do so at the moment, and if we only succeed with one goal difference, somehow we succeed. That's part of Trapattoni's football-philosophy and that may be vital for us to clinch the long awaited title if things go well this year.
The the "italian fox", footballknowledge aside, has personal class to offer goes as an undisputed fact I think.