Efficiency is a tricky thing. If you plotted the force/draw curve of all four bows (a compound, modern recurve, modern longbow, and a long selfbow), the modern recurve actually stores the most energy, where as the compound stores the LEAST, and if the selfbow is built well enough, it would actually store more than the modern longbow (though, it would be the lower with a good modern longbow, or poor craftsmanship). However, the compound's design allows it to crank out blistering speeds, which create high KE numbers. This is why an 80# compound can shoot 525 grain arrows and not need a stabilizer, sitting gently in the hand. It sotres less energy. Try this with a same weight recurve or longbow, and you would have to raise the rbace height to about 9" to lower the handshock and noise.
What's it all mean?
You need to use the right point and arrow weight. For traditional bows, you'd be best served, for hutning, with wooden arrows, or weighted carbon or aluminum arrows. The compound should be shooting arrows slightly heavier than some shoot (something aorund 400-500 grains will be better than a 300 grain, basically flight arrow).
Once you have the proper weight arrows, the point will be the final determining factor. Here, speed is what determines the point. Higher speeds produce, with similiar arrows, the higher KE. KE bascially means a harder "punch". So, for the extremely high KE compound, Muzzy points with chisel tips, very small, vented blades, and field-point type accuracy will be the best serve. These would destroy and should or bone they encounter, and the three or four blades would do a fair bit of damage passing though, despite their small diameter.
For the modern recurve, three blade points, especially the Wensel Woodsman and to a lesser extent the Snuffer, would work best. These points would land home very hard, and tear an incredible hole. With heavy arrows and cut on contact three blade heads, this bow would kill just as quickly, and possibly more so, than the same weight compound. The ony difference here would be the ease of accuracy.
Now for longbows. Faster modern longbows seem to float in limbo. They aren't usually as quick as modern recurves, but for the most part faster than the selfbows. So it will depend on your bow which points it would be better served with. Anyway, selfbows and lesser modern longbows should be shooting good, heavy arrows like the recurve, but their points must be better selected. Magnus, Zwickey, Razorheads, and Hill heads, as well as trade points and knapped heads, all have only two blades, a sharp cut-on-contact tip beign a must. Three blade points here would impede penetration too much to make up for the extra damage. A point that easily penetrates deeply, even at the cost of the extra damage of a third blade, would be the best choice. I don't have enough experience and haven't talked with enough people who've used them to know where they would pit in with all this. Perhaps they would be best with the limbo modern longbows?
This all just ties in with what Viper and DwayneR already said, and nothing makes up for good accuracy. Such a standard is perfect, and might be why they don't feel non-compounds can cut it. Most traditional archers accept their "limits" even when practicing, and set boundries, and don't push them even when practice. Hence the lack of Howard Hill type shots now. Not that we should emulate all of his ethics, but his accuracy and determination would help improve many a shooter. It's not our weapons, it's us.