IMHO Michelin soft terrain S-12s are probably your best all around tire choice for off-road woods riding, 2-stroke or 4-stoke. They wear like iron.
Michelin's medium terrain M-12s are excellent for mud and medium to harder surfaces. The M-12s respond very well to "4-stroke engine braking."
Both the S-12 and M-12 rear tires are considered directional although the S-12 can be "flipped" without any problems. The M-12 is definately a directional tire.
After choosing any brand of tire, sizing is probably the most important issue.
If you're riding a 400 to 450cc thumper using a smaller size tire (120/90) can give you more "2-stroke like" power delivery (easier tire spin) while a bigger, heavier (140/80) tire can help put the 4-stroke's "torque" to the ground better.
Steve