Rasengan is like a hammer used for destruction while the chidori is like a sword used for cutting through things and slashing things. Tailed beast rasengan is stronger then the curse mark chidori because the nine tails chakra is stronger and more massive then Sasuke's curse mark.
The Chidori was created by Kakashi Hatake after he failed to apply his lightning-nature to the Rasengan. He intended for the Chidori to be a weapon used only to protect friends and loved ones.
Although strong, the Chidori doesn't really hold up well against the Rasengan, as seen when both Naruto and Sasuke tried out their Jutsu during the original series.
While the Chidori might be the better and more useful of the two techniques, the Rasengan is certainly more powerful. Chidori is a very powerful technique that can be extremely useful in a fight, and it has killed a lot of people, but Rasengan would win in a direct clash.
So logically you would think rasengan is harder to master. However there are many factors that went into learning both of them. Sasuke had the sharingan which significantly decreased the amount of time required to learn chidori, not to mention he had an affinity for lightning.
Naruto Uzumaki
Evidently, Naruto managed to accomplish what his father couldn't, and eventually completed the Rasengan. The yellow-haired protagonist is arguably the most extensive user of the Rasengan in Naruto, having managed to create multiple forms of the technique.
The Chidori was created by Kakashi Hatake after he failed to apply his lightning-nature to the Rasengan. He intended for the Chidori to be a weapon used only to protect friends and loved ones.
Surprisingly, Kakashi is also one of the many users of the Rasengan. In fact, he mastered this technique at quite a young age. Just like Minato, Kakashi tried to add his nature transformation to this jutsu to perfect it, however, he failed. Interestingly, this is how he came up with the Chidori instead.
However, Naruto's lack of any visual prowess wasn't the only reason for him to not master this special ability. His signature technique, the Rasengan, was based on a physical feel, as opposed to the Chidori, which was more suitable for the Sharingan.
1 Sasuke Uchiha
Sasuke Uchiha is the strongest known lightning style user in the Naruto series. Like Kakashi, his go-to Jutsu is the Chidori. However, his arsenal is much more diverse when it comes to Jutsu.
Although the Rasenshuriken can destroy the opponents at a cellular level with countless cuts, it also damages Naruto's chakra system. As such, this technique was forbidden by Tsunade Senju, the Fifth Hokage.
Sasuke can't copy the Rasengan because it has no hand seals which the Sharingan needs for it to copy jutsu. However there's nothing really stopping him just learning it the old fashioned way if he wanted to.
After losing his Sharingan in Naruto, Kakashi replaced Chidori with its lightning-based counterpart named Purple Lightning, which is nearly identical but without the speed boost and piercing power. Unlike Chidori, Kakashi is able to use Purple Lightning in both close and long-range fights.
The Sharingan was mainly used for casting Genjutsu, following an opponent's moves, which could be the hand signs they make, and to imitate the opponent. Sasuke couldn't just "copy" the Rasengan, he would of had to master it too.
1 Super-Ultra-Big Ball Rasengan
The Super-Ultra-Big Ball Rasengan is one of Naruto Uzumaki's latest techniques that he developed in the Boruto series. This technique debuted during his fight against Delta and while Delta countered nearly everything that Naruto threw her way, she wasn't able to deal with this technique.
Minato excelled at multiple things, including ninjutsu but speed was certainly his biggest asset. He was known to be the fastest ninja of his era and he was much faster than the likes of Ay, even in his natural speed.
By adulthood, Lee had mastered all eight gates. In the anime, Metal Lee, Rock Lee's son, is shown subconsciously opening the first gate. Kakashi Hatake is seemingly able to open the first gate, as seen when he activates it during a Cliff Climbing Practice. The anime later shows him opening it explicitly.
Chidori is a jutsu that stems from Rasengan. In other words, Rasengan is technically the first step of Chidori in terms of its creation. This is why Kakashi knows how to use Rasengan aswell. The Chidori is a failed vanishing rasengan in every way.
Ninjutsu. Minato was taught by Jiraiya how to (Summoning Technique) summon toads, and was one of the few people to earn the respect and full cooperation of Gamabunta. He demonstrated skill with barrier ninjutsu and could use the Shadow Clone Technique.
Similar to other Mangekyō Sharingan abilities, Susanoo was taken from Japanese mythology: Susanoo is the wild god of sea and storms, brother to Amaterasu and Tsukuyomi. He was born from Izanagi washing his nose.
The Rasengan is a powerful A-rank technique invented by the Fourth Hokage, Minato Namikaze, which he created by observing the Tailed Beast Ball.
Jiraiya is a ninja from the village of Konohagakure trained by Hiruzen Sarutobi, the Third Hokage. He becomes known as the "Toad Sage" due to his training under the Great Toad Sage in the field of Senjutsu (仙術, lit. "sage techniques"), enabling him to summon toads as allies during battles.
It is said that Minato did teach Kakashi the Rasengan, and respectively, The Chidori was created as Kakashi only applied his lightning release/nature to it.