When faced with a bunch of different vague tradeoffs like this go with a 'which has the lowest total cost of ownership?
Starting at that, then try to internalize the issues involved in making is sustainable.
Wooden pencil: Made of cedar. Cedar logging in North America has some stringent requirements for erosion prevention, and regeneration. Graphite and clay are not resources in short supply. No costs to internalize.
Plastic mechanical pencil: Probably made of styrene. Styrene monomer is made from natural gas. Styrene is also an easily recycled plastic.
In addition the cheap plastic ones typically come with several chunks of 'lead', and can be refilled. The usual limitation I find is that they get lost before they break down. Because of their clip, and shorter length, I don't lose them as fast. Often a 12 pack at staples is cheaper than a similar box of wooden pencils.
Finally some value needs to be given to not having to sharpen them.
Overall: I would go with the mechanical pencil. But you realize that you have been more unsustainable by driving your car to the end of the driveway than any reasonable number of pencils you use in a year.
One last consideration. The mechanical pencils are more agile. All writing instruments have a flight reflex that kicks in at the sound of a phone ringing. If it can't run or hide, it has "pigment constipation" and will refuse to write. It may be that these are older, and sacrifice them so the others can get away.
