Quickest walking route to jardin des plantes

According to Google maps, it is about the same from both

And why wouldn't you just run this on google maps yourself rather than asking strangers on line to do it for you?

While I'm sure that Google maps is helpful regarding distance, I don't think it helps with the ease (as you inquired about also) of the different metros. Some have more stairs than others, etc. I'm hoping that there are those here who can help you with that.

I've walked from the Jardin des Plantes to the Austerlitz Metro entrance and it is literally right across the street. Quai de la Rapee is on line 5 which I don't have occasion to use so have never walked to that station but it's across the river.

I'd go with Austerlitz, all things being equal. I don't remember a lot of stairs down to Line 10 which was my aim. You'd also avoid crossing a busy street.