What makes a visual approach quicker than an ILS approach?
Visual approaches can be conducted from any point around the airport where the runway is in sight, e.g. if you are approaching from the north of the airport, you can be vectored to a position which is closer to the airport and be cleared for a visual approach from a position where you can turn visually and reach the runway threshold.
ILS approaches begin at the approach gate before the final approach fix (FAF) for the localizer and glidepath indications to be correctly used and the aircraft configured for the approach. The FAF is at many airport around 10 NM from the runway threshold at 3.000ft AGL, thus placing the approach gate at around 12-14 NM.
A pilot on a forum has summed it up like this:

Visual approaches are usually shorter than instrument approaches. By that, I mean that the turn to final is accomplished closer to the runway when on a visual approach.
When traffic is heavier, or weather is around, or it's hazy, smoggy, etc, ATC will usually route everyone out for an ILS.
Many times, a pilot will call runway in sight, yet be sequenced behind someone who is on the ILS. So, he'll get routed out for an ILS approach, even though he'll go visual within the cockpit.
Airport size doesn't have a whole lot to do with it. Also, even though an aircraft may be on a visual approach, that does not absolve ATC of separation resposibility.

(Source: www.airliners.net - Author: Tom in NO)
Effectively, this means that visual approaches tend to be shorter and quicker than ILS approaches with vectors to the FAF/approach gate.