What’s Your Parenting Style? Relaxed or Paranoid?

My wife and I have very different parenting styles. Maybe it’s a Mom versus Dad thing. My wife is always very concerned about what the kids are up to, constantly envisioning worst case scenarios and worrying about every sound or lack thereof. Me, on the other hand scan the perimeter, assess hazards and let them loose. I’m not inattentive to them, just hands off in their play. If they fall off the couch or make a huge mess I deal with it afterwards, soothing a bump or making them clean up their miss with my help.
When we’re out in public, I tend to let the kids run free provided there aren’t too many people or hazards (sidewalks close to the road for example). I don’t let them out of my sight but I’ll let them run ahead or lag behind at their leisure.
Their Mom wants them to hold her hand or ride in the stroller most of the time and she never lets them be more than five feet away. She also gets nervous if they are in a different room than she is and a different floor of the house, forget it. When it’s just me, they get free range.
If they want to play in our fenced and locked backyard that’s fine too, I crack a window and get some stuff done and check on them every few minutes.
Now, I’m not saying that my wife is smothering or I’m neglectful, we are more centered in that scale, just she leans one way and I the other. I have noticed though that our kids act very differently when their mom is around, they tend to push their luck, with me they do their thing and rarely consider leaping off the top of the stairs or clearing every object off of every surface of the house.
What kind of parent are you? Do you find you’re different from your spouse? Do your kids act differently with them?