My take on plywood. It's complicated. Actually, plywood rating is a mess. When you go to a lumberyard, and ask for "marine ply" they are likely to sell you fir made with boilproof glue, which is likely to be a melamine or phenolic glue. From what I understand, there are different grades of melamine glue, some better grades lasting longer in the boil. Phenolic is more expensive and better, basically permanent. Also, this type of fir plywood usually has fewer plies per given thickness of plywood. It can have knots, or knotholes filled with putty, or voids. In my experience, this fir will crack and check over time, even with epoxy encapsulation.
My choice in wood for boating is BS1088 grade, or BS6566 grade. This will be made with boilproof glue, hopefully higher quality phenolic glue. It will also have a greater quantity of thinner plies per given thickness of the plywood. There should be no voids, and no holes filled with putty. BS1088 has higher quality faces than BS6566. So, if it's not really visible structural plywood, BS6566 ought to do fine.
Okoume tends to be fairly light in color, with a somewhat non-descript grain pattern (as compared to real mahogany or teak.) Okoume isn't the most rot resistant tropical hardwood, so it's recommended to be epoxy encapsulated. Meranti can be all kinds of colors, and grain patterns, kinda the luck of the draw what your panel looks like. I have heard that meranti tends to be more brittle and can splinter more easily. I think this would be an issue more with sawing it and working it, than anything else. Sapele plywood is pretty expensive compared to the other two, but can have amazing and dramatic grain patterns, and so is favored for brightwork visible applications.
I hope this helps some. Of course, it doesn't answer the OP's question of "Which is better, okoume or meranti?" I have worked with okoume and sapele building a stitch and glue kayak, and okoume for other applications, with no problems. I have not worked with meranti. I think that probably either of the 3 varieties will give you a solid bulkhead. Sapele would be the more expensive option, but would probably give some pretty grain for varnishing. Or, you could buy some teak faced plywood.
Further investigation with noahsmarine.com gives pricing as follows for 1 sheet 12mm thickness BS1088, meranti $110 USD; okoume $114; and Teak with 2 good faces $228.

Sapele seems only available in 4mm for $89 USD or 6mm, so you won't be making sapele bulkheads...