I think there's a good way to choose. If it's a continuous period, It's more natural to break it down into days, hours etc.
For example, the age of a forum post. You're measuring time-span as a continuous period, so when you look at a comment and it says "2 years, 3 months old" that's easy to get your head around. However, 10,223 hours makes it very difficult to work out (and beyond a certain time, just a year/month/day would be more natural).
However, as people have mentioned, you're not dealing with a continuous time-period - but a "ticker" measurement. It's a log of time spent playing the game, not a measure of period.
Does 125 days of playing mean I first played the game 125 days ago and I've been playing it regularly since? If it says 10 days, and I play an hour a day on average, is it saying I've played 10 hours? Does it assume a day is 8 hours?
I have to say, it's also what gamers are used to. I've heard gamers talk about playtime in hours. "I've logged over two hundred hours in Kerbal and not even got past the moon". It's easy to compare with others as a single metric.
I'd stick with steam's method.