power boosts
which is better,bleach's:bankai, dbz's:kaioken(1-20), naruto's: sage mode
remember kaioken can be enhanced as much as the body can remain stable sage mode takes time to use but has the advantage of using natural chakra from outside the body and bankai it pretty limited but allows the use of a zanpaktos special ability
Ichigo's gets the greatest increase of all Bankais in stats and output from Shikai. His Bankai makes him 2x as fast and around 3+x as powerful. Bankai gives the lowest boost and is safe, other Bankais gain a higher level of their ability but don't amp the character physically as much as Ichigo's.
Sage mode makes Naruto 4x faster and 5x as powerful, is much more durable, can sense chakra and extra range in his melee attacks. Though he gains a limit on his Rasenshurikens use and has a has a relatively short time limit and needs clone reserves to make it useful in combat, doing so limits how many clones he can make.
Kaiokenx20 increases Goku's speed and power by 20x. Drawbacks is that it lasts for a extremely short while and heavily damages the body, more so for higher levels with the risk of death with the highest level. Kaioken gives the highest boost but has the most limits and dangers.
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Which one is better depends on the usage. Bankai for the endurance of a long fight, Kaioken for an emergency situation, Sage mode is a balance between the two. I'd say Sage mode for being more useful while not that detrimental.
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For the best of their full power boosts; Full Bijuu mode > SS3 > Final Getsuga Tensho.
Ichigo got more of a speed increase than just a doubling.
In with his Shikai he couldn't react to Byakuya's Bankai. With his Bankai he easily reacted to Byakuya's Bankai even when he was using his hands which doubled the speed, and Ichigo still wasn't going all-out. So it's more than just a doubling in speed at that time.
Now it would still be faulty to say that it's always a doubling because it could well add a static increase, which at the time just happen to more than double his speed.
I didn't feel that the Sage Mode made Naruto any faster, it clearly made him more durable and stronger, but even when it wore off he could react to Pain's kick.
Kaio-ken is probably the worst. It's a multiplier of speed and power -- whatever power means -- but it can only be used for an instant, and by someone who's really strong to begin with.
So if I could chose one it would definitely be Ichigo's Bankai, followed by Sage Mode, and I'd be hesitant to even get Kaio-ken because it might be tempting to use at some point and I might accidently kill myself.