There's no computational issues behind using a different time scale. I would make sure the time scale you used is biologically/practically meaningful and plausible to collect. If you're talking about the time-to-failure of a single node in a computer cluster, you might be able to say you'd know the event time down to a fraction of a second. If you're talking about time until HIV seroconversion, you'd be lucky to know the day, and more likely know the week or month. Simulation studies are most useful when they're conducted similarly.
I wouldn't worry to much about ties in your time - they'll happen in real-life too, and its useful for your situation to know how to handle them.
So I'd say, generally, pick a good, interpretable time scale, and retain as much precision as is reasonable in a real-world setting.