The cannon is a chakra weapon used by the Hidden Cloud to defend against some of the meteorites. It was supposedly strong enough to destroy other villages, and potentially strong enough to destroy the moon, but didn't because Naruto and the others were there, rescuing Hanabi. Destroying it during that time would pit them against Konoha.
The Tenseigan was a weapon that used a thousand years' worth of byakugans' eye powers. It could supposedly obliterate earth if powered up. Toneri didn't have eyes, and needed a Hamura Descendent's eye to wield the weapon's power. He tried to go for Hinata, but when he couldn't get her, settled with Hanabi's eyes.
This, along with some unmentioned scenes, left him with the Tenseigan (eye), and the eye's Chakra Mode. This enhanced form of the Byakugan was on par with, or stronger than the Rinnegan (whether it's base rinnegan or rinnesharingan is unclear), and the Tenseigan Chakra Mode gave him power at least on par with Uchiha Madara.
It must be noted that his Tenseigan was rather unstable, with it paining him from the time to time (even during his fight). It may either be a side effect of the eyes, or may be because he was using Hanabi's eyes instead of Hinata's (who was supposedly Hamura's transmigrant).
More on the weapon:
The Tenseigan Weapon is supposedly a railgun-type beam. The beam dealt the same amount of damage throughout its length, and can't be "interrupted". If it was strong enough to destroy a rock, it would be strong enough to destroy the whole earth, by this logic. However, its ambient damage wasn't particularly high, as Naruto could tank it with Kurama's Chakra. Basically, it's strong enough to destroy earth, but can be 'tanked', but not 'blocked' by chakra cloaks and other means. Railguns are complex.
More on Kaguya's Army
It has already been known that Ootsutsuki were an alien clan. Back in their planet, they (or atleast one of their branches), may have experimented with the Tenseigan. Having seen its power, she may have wanted a way to stop it, thus took the rest of her clan and left their planet in search of large amounts of chakra. She found this on Earth, hidden within a fruit, which she could see because of her Byakugan. She needed a ruthless, obedient army to counter the Tenseigan back in her home world, but normal humans weren't either, and the average person couldn't fight. Thus, she came up with the Zetsu plan.
What may have actually happened with it is unknown, but Hamura apparently learned of it, and used it as inspiration to make an even stronger version, thus the settlement on the moon. I believe the original Tenseigan has since been destroyed, and the original ootsutsuki members killed/extinct due to infighting or a zombie apocalypse of something.
Note: Hagoromo's legacy was devided into his Eyes and his Body. The Ootsutuki legacy is the same: Tenseigan (Thousands of Eyes), and Zetsu Army (Thousands of Bodies).
Just a theory I've been working on. Any plot-holes so far?
