I made a set of crutches and I want the height to be adjustable both at the handle and the base. Would this be better to be done with parented props with limited movement or rigging?

As an end user, I think rigging it would be much simpler. Parenting stuff sounds like it might be confusing and complicating.

Could you make it a morphing prop?

I would do like this for the most flexibility.

You make each of the highlighted parts, including the grey mesh an individual part. Then you make the red and green a child of the grey mesh, and then make the grey mesh a child of the blue handle, so it will be the controlling one. This will allow the user to adjust the red, green, grey mesh parts so it fits different characters. The green area, simply shows that if you add two extensions that go into the grey mesh they should be slightly smaller than the grey mesh so it looks like it goes into the mesh. The yellow line is just a suggestion of where you can cut the grey mesh so the green extensions are visible.

Then you set some limits for each of the parts according to how they should be able to move, hide those translations that the user shouldn't be able to adjust. (You can make the grey mesh and the blue handle as one object if you don't want that much flexibility.)

When you import it into Poser, you make sure that the crutch matches the T pose of a character (meaning it is laying horizontally) so the blue handle fits the hand as best as possible with the green handle under the shoulder, that way the user can easily move it to fit whatever character they use. Then all they have to do is to parent the blue handle to the hand.

Hope it makes sense :) It is very easy to do and use despite sounding a bit complicated.