When Sasuke first activated the Susanoo with 2 MS it didn't really resemble the Complete Susanoo. But when Obito gave Kakashi his eyes he activated Complete Susanoo. Why did it take so long for Sasuke to activate Complete Susanoo.
Once a user awakens the Mangekyō in both eyes, or the ability of both of their eyes, they are able to perform Susanoo.
Sasuke could make a "perfect" Susanoo once he got ability of both of his eyes. One probable reason why he didn't use it right away could be the fact that Susanoo does use up a lot of chakra and he might be saving his chakra.
The Mangekyō Sharingan's abilities drain a considerable amount of chakra when performed.
This perfect susanoo is only available to those who perfectly master the mangekyou sharingan. Kakashi had the benefit of mastering one eye while obito mastered the other and when obito died and loaned those eyes, it was as if both obito and kakashi's experience was applied and as suck, they just had to awaken the susanoo in that state, while sasuke had to master not just his abilities but also those of itachi to awaken the susanoo perfect state, essentially having to master two pairs of susanoo. And interesting fact, that s shows that no matter the person, as long as a mangekyou sharingan is implanted, they can attain the eternal mangekyou sharingan as the perfect susanoo would likely blind the user of a regualar mangekyou sharingan instantly unless we speak about the pure sharingan of hagoromo and Indra. Or they may already be blind at that point due to practicing the mangekyou which requires regular use.