I'd like to know if both side are in perfect plane where they meet. Very important.
I don't like either method your masons suggested, (masons, why masons to set tiles?), but some clarification is needed in the first method.
• One mason suggested 1/2 plywood with a wire mesh on top (no membrane) then "mud" into which we'd set the ceramic tile, which he sez can be used to level out remaining inconsistencies.
The term "mud" is sometimes thrown out to confuse. Mud in tilework is a mix of sand and Portland cement placed about 3/4"-1 1/2" thick, or thicker, as the base for tiles. However, often the word "mud" is used when thin set mortar is used instead. Thin set is the adhesive used to bond tiles in either case, it is NOT "mud".
It sounds as if you've been told about what is know as a "Jersey Mud Job", it's not a good thing. Please let us know more about what he was proposing with this method.
• Another recommends 1/2 inch Wonderboard. Is Wonderboard as good as the 1/2" plywood?
You can NOT install any tile backer direct over plank subfloors or on a concrete slab.
So, let me know if the two areas are in plane in which case I'll most likely again suggest replacing the planks with 3/4" ply and then using a membrane over both.