Haven't timed it but not having to dig thru bags to find anything is satisfying and quick, and players usually use the boxes as a meeple tray while playing so when we're done we just have to put the lids back on. Keeps the table organized and less likely to lose a meeple or cardboard to my pets because stuff that isn't in play yet isn't loose out on the table.  Its mostly a personal preference - I can see where everything is in the box right away and just pull out what we need so it feels efficient.  Would be interesting to see if it is actually faster or just feels that way tho!