I've done some of both. Daytime driving is on average easier and more pleasant driving, although night driving can be quite enjoyable under the right conditions (limited traffic, decent moonlight, and reasonable weather help a lot). "Driving" in cities during rush hour is an obvious exception (when there's more sitting or crawling than driving).
If time is limited, I sometimes find it works reasonably well for me to drive overnight in shifts interspersed with sleeping for a few hours at e.g. a rest area. Without time constraints, though, I would not generally do so by choice; sleep is better and life more pleasant staying the night somewhere, especially if that somewhere is a nice campsite.