Laurence Griffiths/Getty Images
Liverpool need a manager, obviously. Now while AVB's time with Chelsea may have been nearly a disaster, I'm really hesitant to blame the young Portuguese manager for that. Really the blame should lay on the ego's of the senior players and a generally unsupportive fan base (although I think they're all Man City fans now).
Liverpool doesn't have the ego issues that Chelsea has. For Chelsea, John Terry is an usurping, power-hungry captain, and Drogba is an aging star who has used his previous achievements to attempt to justify an astronomical arrogance. Liverpool instead have Jamie Carragher, a leader loyal to the club and supportive of managers, and Steven Gerrard, equally loyal and supportive, along with being more realistic, exuding confidence and class—not arrogance and pomp.
Also, Chelsea's players and play style is completely at odds with AVB's. Chelsea favors a direct, often defensive counter-attacking style with big passes and pace down the wings. AVB prefers a fast, technical, more offensive passing game.
This is a style which marries very well with Liverpool's pass and move, and if you really need proof, look at the South American and Spanish players who have played, and those who still play at the club. They have adapted well to the club's style simply by making small adjustments to their normal technical, ground-based game.
Villas-Boas does not generally use traditional wingers, preferring more inside-forward-type players in his preferred 4-1-2-3. This also plays to Liverpool's strengths—or rather sidesteps its weaknesses. Liverpool has had horrible wingers for a while now, so why not just change the tactics to not emphasize wing play?
Finally, Villas-Boas has strong beliefs in the strength of young players. Only a Liver bird defecating on a Manchester United shirt could be more "Liverpool" than utilization of youth.
And with the potential in Shelvey, Henderson, Coates and more in the youth team, it's a great time to bring in someone who appreciates that ability.