Aye frankfast,
I believe that the 250 scrambler cam (White), if indeed that is what it is, is a 'softer' cam than the green and white cam.
My understanding is that the more valve overlap timing and lift the cam profile gives, the more stress that you are going to put on the interface between the rockers and the valve stem. Hence, whilst the threaded and locknut adjustable tappets are easier to maintain, they are more likely to succumb to higher stress input, than the shim.
Regardless, of cam, I believe that the shimmed rockers are going to be more stable and less likely to move out of adjustment than the threaded and nut locked adjusters. If all you have are the adjustable tappets and you want reliability, don't go mad with the cam timing and lift. If you have a lumpy cam and only adjustable tappets, you can still use them, but be prepared for them to require checking and adjustment more frequently than the shimmed version.
After all, 350 Sebrings used to have their necks rung, with green and white, or radical "one off" cams and adjustable tappets.
As for the working clearance between the tappet/shim and the valve stem, I believe that is influenced by the shape of the cam. Stick to the manufacturer's recommendations. Making it larger than recommended, increases the 'hammering' effect of the rocker on the valve stem. Whilst reducing the recommended clearance increases the risk of the valve not closing or even being battered by the piston. Neither of which are benificial for engine longevity!
If any of this is incorrect, I apologise and will be happy to take on board others opinion with more experience.
Good health, Bill