A:Answer You'll have more gesture options available with the apple mouse, mainly one/two fingers double-tap and left right swipes similar as on the trackpad, something you might get used to but not essential, some other Logitech mouses have forward and backward buttons can serve similarly.
Apple mouse is rechargeable.
Both are pretty flat, so they aren't ergonomic comparing to other Logitech mouses. I often hold the apple mouse in 45 degrees because of its shape and end-up right clicks a lot by mistake.