Communications with others are expressed as a written or spoken number. But then calculations with that number (eg. "how long do I have?") have to be done with arithmetic. It's fairly rare that I wear a watch, but when I do, such as at a conference or similar, I prefer an analogue face. In this kind of case I prefer to visualise the time on the clock face. Then I can "see" the time remaining without doing arithmetic.

> If the latter, why does skipping that extra conversion step by using a digital watch feel worse from your perspective?

I'm quite capable of doing it either way, but my preference is to do the single required conversion to "analogue" so that repeated comparisons are visual and do not require repeated arithmetic. I also find it easier to remember a time visually, whereas single-digit errors in remembering a digital time can result in a greater error.