Reality aside, it also depends on the shape of the river. With that kind of current, you’re pretty much guaranteed to get swept through many curves of the river, which affects the horizontal distance you have to swim.

Real rivers that are fast are usually turbulent.

Real streams that are not turbulent aren’t any harder to swim across; you aren’t aware of the stream’s movement, and may be surprised how far it carried you (after a short swim across). Try it with an ocean current sometimes. Just make sure you survive the experience!

Can you guys agree on a way to settle the argument?

We’re basically negotiating on terms, same as everybody in this thread. Depending on where we put the goalposts for statistical significance, either one of us is right. She’s right that, on balance, I’d rather swim through still than choppy water. So in that sense the fast-moving is harder. But I’m right that it wouldn’t take that much longer. Particularly stacked against what our intuition tells us would happen in the fast-moving water. So we agree to disagree and go get a beer.