You don't understand how Chidori works. Let me dumb the differences between the two down for you.
Chidori is nothing more than lightning chakra with shape transformation applied. Rasengan, unlike every other nature-based ninjutsu, lacks a nature (duh) and only comprises raw, concentrated chakra. To concentrate this chakra to such a degree requires amazing chakra control. Chidori, on the other hand, appears as unstabilized lightning because it's just that. As sad as it is, Sasuke was never able to achieve Chidori's higher form, Raikiri, by concentrating and increasing its striking power.
Let's simplify it even more:
Chidori - out of control lightning (pretty high chakra control)
Raikiri - concentrated lighting, hence its more stabilized appearance (expert chakra control)
Rasengan - complete stabilization, hence it's spherical shape (almost master chakra control)
Do you know why Rasengan did more damage to the water tank it hit in contrast to Chidori on top of the hospital building in part 1? Because all of its force was concentrated and compressed towards to centre of the water tank it hit, while Chidori just went through the tank it hit like a fist does a face.
LOL I'm sorry but that's complete bullshit.
Both Kakashi and Sasuke are using the exact same jutsu, which is essentially Chidori.
Raikiri is the nickname Kakashi's jutsu got after he pierced a lightning bolt on one occasion, but its still the same jutsu.
In part 1, Kakashi's version was more concentrated and enhanced because he had better mastery of the jutsu than Sasuke.
In part 2, Sasuke showed extreme mastery of Chidori as he displayed many different varients including chidori sword and chidori spear, so he actually surpassed Kakashi in its mastery, just like how Naruto managed to surpass Minato in Rasengan mastery, both were elevating their signatures moves as shown in every time they clash.
By the end of the manga Sasuke's Chidori is most definitely superior to Kakashi's, and let's not even get started on Sasuke's scene from The Last, its ironic how he saved his sensei using a highly improved version of the jutsu he was taught by him.
"Raikiri" is just a synonym, its not a different jutsu.
OT: standing/walking on water is a basic ninja skill, probably learnt it off screen, its so fundamental and basic its not relevant to show it.