MatisseMonster was undoubtably one of the better series during 2004 and is likely to be right up there as one of the 'best' series for its demographic. However, I personally felt that Juuni Kokki, Moribito: Guardian of the Spirit, Escaflowne, Serial Experiments Lain, Blood+, Paranoia Agent, the Ghost in the Shell series (Stand Alone Complex) and the Ghibli films, to name but a few, were 'better' for their respective genres, amongst many others. It's important to realize that whilst Monster held many qualities, I received an equal, if not larger, appreciation (for different reasons) for other series, of which I've certainly seen my fair share (hundreds, verging into the thousands).
I also felt that Monster became rather episodic and longwinded during the midsection and could have served better with less backstory, that didn't seem to amount to much in the end. The characters are likable, to an extent, particularly that of Tenma and Anna/Nina but the rest, including the infamous Johan, just seemed contrived, despite his initial mystique. I place a large emphasis on overall enjoyment when judging a series. Monster delivered that enjoyment, absolutely, but not in the same way as many others did. For that reason alone, I'll never judge a series as 'best', when its so distinct in its own genre.