Woodlieghs are hard to find in Wyoming and very expensive when you do. So my experience with them is very limited and I personally have never killed any animal with any Woodleigh, but I have seen it done 4 times. Never with a 30-06 and never with that particular bullet.

BUT... I have to guess the results would be very similar to other high quality bullets of the same weight and speed fired from a 30-06.
What I have used with excellent success from 30-06s in the past are the 220 grain Nosler Partitions and the 200 grain Nosler Partitions. In addition I have used standard "cup-and-core" Hornady 220 grain and Sierra 220 grain bullets. I have shot deer, bear and elk with them so the game has run from about 125 pounds to about 875 pounds. Of the 4 I listed above the Hornady 220 RN is the "worst" and it was still very good. The 220 RN Sierra being a little better and the 2 Partitions even better still. I have no doubt at all the 200 or 220 grain Woodleighs would be excellent from your 30-06.

Too may people have been lead to believe a faster bullet is "better" and in my 50+ years of hunting I have not found that to be universally true. Big bullet that hold together and impact at speeds from 1800 to 2300 FPS seem to be at least as deadly as the faster bullets and often better. The "Electric Shock" we see with super fast bullets in not uniform and sometimes it works well, sometimes it doesn't, and when it doesn't the lack of exits and/or deep penetration can and does work against you at times.

My experience with 200 and 220 grain 30 cals have all been from 30-06, 300 Win mag, 300 H&H and 308 Norma. But the 30-06 is the one I used with those bullet the most, and I have zero to complain about. I'd bet the Woodleighs would be as good as the Noslers. I would not hesitate to load them if I could get them or afford them.

Just as a side note: I live and hunt in places that have the largest concentrations of Grizzly Bears in the world per square mile. One rifle that I often carry when I am out there is an M1 Garand loaded with 220 grain RN bullets which I load with charges of 3031 powder so the port pressure is perfect for the old M1. The muzzle velocity is "only" about 2375 FPS. But I have used that rifle and load to kill large elk, deer and black bear, and the penetration is wonderful, and bone is not a problem. I have never shot a grizzly with one but black bear and elk are laid low with them and I trust my life to them. Many men seem to not think of the old M1 as a "dangerous game rifle" but I point out that hordes of Japanese, German, Korean and Chinese soldiers fanatically bent on killing you DO qualify as dangerous. The M1 need not offer any apologies for such a classification.

So, for big bears and other game up to about 1000 pounds I'd say if the Woodleigh is in the same class, saying I'd trust one for that kind of situation would be noteworthy.

Are the as good? I don't know, but some folks here may have shot both Partitions and Woodleighs and be able to tell you.