There are several issues with the videos you posted that have to be considered before taking them at face value.
1st - ak47/wakizashi/sword. There's a few things you don't get to see well from that video such as how long it actually takes him to get that tree down, the shock type to the hands, and the fatigue rate. Because there's a cut/edit in the video, he may have had to rest because he was too fatigued to do it in one shot. He was baseball batting that tree with a lot of energy to get the kind of penetration he was getting. Fun, but not efficient and not a good idea if you are ever going to use it in a situation where you *need* that wood. Efficiency and safety are paramount to survival. Swords are inefficient and uncomfortable to chop with. You should never 'push' into the wood your chopping like you see in that video - all of the momentum on a long handled edged object should be in a pendulum type like you get with an axe, or it should be one handed. Pushing sword style is mostly wasted energy because you can't push cut through wood fibers - all the energy of the forward grip hand goes into pushing against the tree, not through it. If you choose to baseball bat it like you wood with an axe your not being efficient because your center of percussion is halfway down the blade, not at the tip where the weight would best be utilized for maximum rotational force delivery. Since it's not efficient to use it two handed, you could use it one handed but it's awkward and uncomfortable - all the way at the bottom of the handle and you run into a lot of shock vibration and inefficiency from striking at the center of the blade. All the way choked up and you've got an awkward portion of handle that strikes the wrist/forearm and you've got a ton of useless weight behind your hand that doesn't help you cut wood.
2nd - 18" ak. I'll only say that I've owned several 18" ang khola's with edges that were half as thin as any of the battle mistresses I've owned, and they are partial tangs (or tapered if they are exposed). The result is something thats more blade heavy with less handle weight and with a more efficient cutting geometry. It's not entirely accurate to assume that an 18" ak is going to directly translate it's performance to a busse equivelant.
3rd - 1311. There's two things wrong with that video as far as assuming it represents the performance of the 1311. One is what KnifeHunter said - it's dead standing wood that may be exceptionally hard. The other thing is the terrible chopping form that guy is using. He strikes the same place multiple times. You can't remove any wood by hitting the same line twice, you just make the cut slightly deeper. Repeat that 10 times and your not only going to make the blade look like it's a poor performer - your going to be exhausted and have accomplished next to nothing. If your dealing with extremely hard wood, make your chip size smaller - but for the sake of your arm and hand *make chips* by cutting v patterns.
I've owned a bme, ffbm, fbmle, hogfsh, hh, ak47, ttkz, Custom shopped ttkz, kz2, Custom shopped kz2 b9, b10 choiless, b11, moab, nmfbm, battle rat, dog father, and 30+ Himalayan imports khukuries/swords. Within the busse family (excluding the axes/hatchets) the 1311 is the single most blade heavy balance I've experienced. It combines that balance with a relatively thin edge (as far as the overbuilt edges bussekins tend to have) a 13" blade and a 3/16" stock to create the best chopper they've made to date. Yes the TTKZ and MOAB will bite deeper because they are significantly heavier - but they are just that, heavy. What marginal gain you get in penetration you lose in greatly increased fatigue rates. Balance is often everything in a knife, and I've held a few busse's that were superbly balanced. The ones that have always stood out to me as being *perfect* were the b9, HOGFSH and 1311. The 1311 is the only bussekin chopper I now own because of every knife that has ever been produced by the three companies (and I've tried nearly all of them) it stands above them all as a complete package heavy chopper. (and because I'm poorer than ever and can have only one.)