Yeah, Serie A started going downhill in 2001. If I remember correctly it was the year that it became apparent that Parma, Fiorentina, Lazio and Roma were having financial difficulties and on the brink of bankruptcy. Inter and Milan were also not financially stable, while not selling off their best players they hung on to them and failed to replace them. Hence Milan's best players only a few years ago were ageing stars from around this era.
I don't think the Premier League became stronger until a few years later though, after Roman Abramovich bought Chelsea. Up until then it was only Man Utd and Arsenal.
And damn, I don't remember Birindelli being that good, could teach Lichtsteiner a few things. The individual quality upfront was definitely better back then (Zidane, Del Piero, Inzaghi), but I actually like our modern play better.