I was thinking about this phenomenon today. Digital clocks are so common now that I don't often need to read an analog one, much less in a hurry. I worry that I'm losing the ability to do so. (The worry is a little bit because I might still need it at some point, and much more because being able to quickly read analog clocks makes me feel like a grown-up.) In particular, when I am called upon to read one, I'm embarrassed by how long it takes me to do so. It's only several seconds, but that's enough to make it clear to anyone watching that I had to stop and think about it.
But then I caught myself, and thought, wait a moment. Am I actually much slower at this than I used to be? Or is reading an analog clock really just a noticeably slower action than reading a digital one? This is intuitively plausible; it has more mental steps. Rather than comparing my current analog-clock-reading speed with a previous one (which I don't really remember), I'm comparing it to my digital-clock-reading speed, which doesn't make sense. I was going to ask how you'd design an experiment to test this. Then I remembered that not everyone is young enough to have to speculate about what it's like not having mostly digital clocks around. :P So if you're old enough to have significantly more practice reading analog clocks than digital, how long does it take you to read one? Is it noticeably longer than reading a digital clock? If you aren't, and have a significantly different experience from mine, I'm interested in that too.
I have always read digital clocks faster. I suppose it is the matter of representation one uses for time. For me, it is always hours:minutes, so when I look at analog clocks, I have to translate. My watch is analog, but there is a small digital display below, and I always look at that display and ignore the analog information, which is confusing for other people, because they sometimes do show different times (the only use for the analog display I have is that it can be used to determine the direction of north, but to do that I do not adjust the analog part to the daylight saving time).
I have to translate in verbal communication, too. The majority who prefer analog clocks usually tell time in format "quarter to eight", while for me it is "19:45". Of course, when I give the time information, I do it in my native format, so they have to translate.
Interesting. I am, as I said, more of a digital-clock-reader, but I still say "quarter of" and "half past" and the like. I attribute this to labels my parents put around the (analog) wall clock in my childhood bedroom, showing where "of" and "to" were, and where "past" and "after" were.
An old SO of mine used to get annoyed when I said "quarter of," though. I wonder if they were so accustomed to digital timekeeping that my habit required an annoying amount of translation for them. The reverse wasn't true, though--I understand "seven forty-five" perfectly.