You have room in your pack for a saw or an ax but not both.
What do you take and why?

I'll start.
Folding saw, 24" length or so and a 4-7" heavy-bladed knife (for batonning decent sized rounds.)
My reasons:
Safer when you are remote and far from first aid.
For me - I can cut more, faster
lighter in the pack. (I have an aluminum setup that folds up to a slim package
Risks/disadvantages as I see 'em:
Saw blades can break. You may be able to re-hang an ax head in the field but making a saw blade... not likely. (Take 2 blades)
I'm sure there are more of both but this is what I can think of at the moment.
Ground rules:
No saw-back axes

Knife considerations are valid and can/should be included

I know this is one of those unanswerable questions but I am interested in your reasons for choosing one over the other. I think arguments can be made for both and sometimes other's experience can point out things we have not thought of.