Leash VS Stroller

So, here is my latest internal debate. I need some help and advice!! I've been trying to think of the least painful ways to travel with kids and have stumbled upon another question... Do I want to get leashes for the kids (otherwise known as 'Child Harness') or should I just stick with the double stroller? Here are the pros and cons that I've thought up:



Stroller:
Pros:
The kids can sleep in it or rest in it as I go from place to place.
I can use it to hang my bag or two on instead of having to carry it everywhere.

Cons:
It can be big and bulky--trying to get it through those stupid X-ray machines at the airport can be a real nightmare!!
We've almost lost it a few times on trips where we didn't know where to pick it up after the flight had landed. (Charles de Gaulle is NOT my favorite airport!!!)
The kids very often would rather run than sit, so I'm stuck pushing around a stroller and trying to chase my kids through a crowd.



Leash (aka Harness):
Pros:
The kids can run/walk to their hearts' content! (and I can breathe easy knowing that they're right there!)
They have cute little backpacks where they can keep a few special things.

Cons:
Will they wear them? and not be angry about it?
If they get tired and don't want to walk, I have to carry them...except I can't.
If they don't want to walk, and I can't carry them, is it kosher to drag them by the leash through an airport?



I've almost been thinking about having both. But, would that be overkill? Am I stressed about this trip? YES!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! I keep thinking that both would be nice in their own way. In Zurich, I have heard there is a fabulous children's play place in the airport, so I think that will help immensely during our 6 hour layover there. In Chicago, we should (hopefully) be able to go straight to our hotel and crash. In Salt Lake...are there still little play places there? And the question is, during our layover there, will the kids want to play? or will they rather run? Is it worth the on and off headaches to bring the stroller with? Please advise!!!!! :)