First I would like to preface that both the positional/solid/quiet openings and sharp/aggressive openings can be played quickly without using much clock time by simply being very knowledgeable about your opening.
Quiet openings, particularly systems, tend to require less time. This is because sharp openings are dynamic, that is to say that every move makes a big difference, something big is on the line. Take the kings gambit for example. The opening could quickly become complex white may have a strong attack; black would be advised to use his time because one misstep will cost the game. White also should take his time to make sure that he/she executes the attack effectively.
Quiet openings, even when played incorrectly, will usually only result in a positional disadvantage, which of course is much less devastating than material advantage that often is in the air when we talk about sharp aggressive lines.
In conclusion, sharp aggressive openings, by definitions, require precise calculation in a forest of complexity and tactics. Positional openings require analysis of positional motifs in the position; this usually requires less time than long strings of calculations that sharp positions such as the sicilian often get.
I draw attention to systems, which almost by definition are openings that the user is able to use in almost any situation. Take the london system, for example. This opening can be played practically against all black openings and quickly as well.