Here is what I'm doing for the parallel world in my fantasy novel (for NaNo). I was using minutes & hours by default, but it occurred to me that it would be more appropriate to alter the system. I've tampered with the structure of days in this world, so naturally the sense of time should be different as well. Here is what I have - what do you think?
As a note, there is a quirk in my world that causes people's physical appearance to change drastically as they age. I won't get into that in this thread, but just know that this quirk allows people to somewhat accurately judge how old they are and how much time they have until they die (in theory).
Quote:
Time of day is judged by the color of the sky. In everyday usage, most time is based on relevance and rough estimates. For more accurate measurements, some cultures use a board painted with the various shades, or beads of the various colors, to hold to the sky and compare. Other regions prefer to use devices such as hourglasses or candles that burn for a certain amount of time; these devices are also used in measuring time during the night. Still other cultures study natural objects such as plants and animals that react to the time of day.
The variety of instruments prevents a unified measurement of time; there is no standard “hour” or “minute.” Some cultures divide the day into even segments, while others measure the time until darkness; for example, the working class in the south often cites “so many miles to darkness,” a folklore reference to how many miles the average man could walk before it was too black to see. For unity, governments often use a standardized hourglass and schedule important meetings on “so many turns of the hourglass from daybreak.” Despite the variance, all units of time are exchangeable by comparing them to the length of the day. The length of day is constant year-round and throughout the earth, with daybreak occurring at the same precise time, allowing for conversion between measurement systems. There is no need for time zones. [In terms of our-world time, each day lasts approx. 12 hours and the night approx. 8.]
Because there is no change of season or solar/lunar phases, the day is the only standard unit by which to track time, making it difficult to charter long distances. Counting days is tedious and old records use number systems long forgotten; as a result, most of history remains untimed. There is no accepted number for how old the earth is, and most cities and civilizations only have a vague idea of how long they have lived. In practical usage, most legends space events by comparing them to other happenings, while cultures time with things familiar to them, such as the life cycle of plants and animals.
While most families keep a record of generations, the average person does not measure how old he is. “Birthdays” and “anniversaries” are not celebrated, and adulthood is judged by physical appearance and maturity according to local custom. Most people rely on their appearance to judge how old they are and how long they have left to live, leading to a careless despondency. The few that do track their precise age are usually obsessed with calculating how much life they have likely left.
Made sense to me. 
