No.
While in a way Windows Phone would qualify to be a stable operating system.
Over the past few months I've been trying to see how true claims about Windows Phone we're. Some people here say Windows Phone never lagged, ran better than Android in low end, never crashed and ran great even when memory was full.
None of those, not even one of those claims has proven true.
Having tried a Lumia 520 and 530, the 530 crashed in my first one minute of using Skype:
http://youtu.be/NEMaxs4-THI
To name a few, Tapatalk, Atmosphere Weather, tons of games, Internet Explorer, Xbox Music, Magnify Newsreader crashed on the 520 in more extended use.
The reason why people say Windows Phone has never crashed for them can also be partly blamed on the fact that Windows Phone doesn't give you any message about why your app just closed, so most people don't realise it.
There are tons of things wrong with scrolling, where content often disappears and takes you back to your original point. Touch issues seem to be apparent.
iOS with Apple's strict control over software and hardware is the most worthy of being called the most stable experience you can find on mobile, Android and Windows Phone would come in second place.