This is not an answer, but rather my attempt at a road map of what you need to know to answer your question.
Much depends on externalities.
Wood is an awfully cheap resource. You plant trees, and mostly ignore the land for 20 to 80 years depending on what you want. (Not quite true: It is usually worth your while to thin about 1/4 of the way through. High value hardwood plywood peeler logs are worth trimming the lower branches to 16 feet once the tree is 24 feet tall.)
Bamboo grows fast, but due to the nodes, I expect that processing it into plywood is more difficult. You need to be able to compare square meters of plywood per hectare per year.
Plywood is a specialized product. There is good reason that most plywood in house construction is now done with oriented strand board -- it's easier to make, and uses up more of the tree.
This in turn means that the relative merits are going to depend on alternate uses for the parts of the tree not used to make the product.
Both wood and bamboo use nutrients from the land. Most softwoods get adequate nitrogen from the air (NOx from lightning, nitrogen fixing plants) but several cycles of forestry and harvest can deplete soils of other elements. Good forestry ideally removes only the usable wood, and leaves the bark, branches, leaves/needles. In some cases this promotes pests, and can require some degree of processing (burning, burying, pesticides...) to complete the cycle.
Another factor is transport. If it fits into a sea can, transport is very low cost on the ocean. But getting from the forest to the plywood plant and from the port to the user can be expensive. These costs however are not external, and will be built into the price.
Another non-external cost is the glue to hold it together. Off hand I don't know why it would be different, but given the variety used in ordinary plywood, it wouldn't surprise me to find that bamboo has different requirements.
Glues however have their on external costs. In production many can produce some pretty ugly byproducts. After production some can outgas undelightful chemicals for some time. (Formaldehyde being one...)
Once you have a list of external costs, you need to put some kind of measure on them. That alone is non-trivial. (How does a pound of formaldehyde released over the first 10 years post process compare to 30% more waste?)