I often find myself climbing with 1 axe and a whippet on many climbs that involve skiing. Unfortunately whippets are not much help on ice as a climbing tool. The "pick" is only really good for keeping your balance on ice, since it rattles around a bit where it's attached to the pole. You can't swing it or anything, but you can hook things with it. It does not replace an axe when one is needed, but I find it gives me just that little extra bit of balance and security in places.
I like whippets for steep skinning or traversing on ice where falling would have serious consequences. In reality, those are the kinds of falls where a whippet will stop you reliably, where you are not going too fast. I have not taken a screaming fall on steep ice, so I can't say if the whippets would help there or not, but they do feel good to have in your hands when you are on steeper things.
They are bloody expensive at retail price. Remember you also need the lower part of the pole to begin with. They do help in lift lines when there is a question on who goes first.
So I guess the question is, what you do most often. Are you climbing more and need a second axe? Are you looking for steeper lines for skiing? They serve different purposes.