Given the caveat that I retired in 1999 and cannot speak for today's pilots, my thinking and the observed preferences of the great majority of the pilots I flew with follow.
With few exceptions, a visual approach was preferred over an ILS for the simple reason that it's usually quicker, and over time in large aircraft, the fuel savings can be significant for your company. I did know a few pilots, though, that liked to stay in the air longer to increase the size of their paycheck when being paid by the flight hour. I always felt this was unprofessional. A 747-100/200 (my airplane for my final 10 years) burns a lot of fuel, and part of the captain's responsibility is not costing the company money if you don't have to. Also, if you have people in the back making connections, you want to maximize the time they'll have to make those connections.
There are times, though, even with CAVU conditions, you may want the ILS. For example, I was offered the visual approach one night into Hunter Army Airfield in Savannah, Georgia. It was my first time there, and locating the runway in the maze of lights made it unwise to accept. In fact, I found that airfield so hard to find visually at night, that I continued asking for the ILS until I had been there several times.
Of course, if it's clear, but you're going into LAX on a hundred mile final from the east with 15 or more aircraft doing the same, you don't even think about a visual.
Generally I followed the practice of requesting a visual approach when first possible going into familiar airports when the traffic was light and there was time to be saved.
There were pilots of foreign airlines that would never request a visual. For example, Japan Air and Korean Air going into Anchorage in the early 1990s always requested an ILS. If it wasn't available, they would request a VOR approach. As I understand it, their training, culture, and experience (as explained to me by a JAL check captain) didn't favor being able to just look at a runway and land.
It's a minor point, but to me visual approaches offered more opportunities to play.