So the same applies here. Itachi is best at Genjutsu that's why he got a power named Tsukuyomi other than a normal Genjutsu.
Similarly Sasuke isn't good at Genjutsu so he possess only Genjutsu. There's no such thing as "WEAK TSUKUYOMI" and "STRONG TSUKUYOMI".
Since Itachi gave a small portion of Amaterasu power to Sasuke in order to kill Tobi, Sasuke awakened Tsukuyomi.
And to talk about Sasuke's Genjutsu, it wasn't even that bad. We all know he beat Orochimaru and Deidara with Genjutsu.
But still he doesn't have a Tsukuyomi.
Since the Tsukuyomi was shown and Itachi mentioned his conditions of getting Susano'o are Amaterasu and Tsukuyomi, most of the people started considering the fact that Sasuke also got the same things.
But when Sasuke used Amaterasu, there was a difficult situation infront of him. Similarly when he extinguished the flames from Karin.
In both the cases, he had difficult situations and there were no other option for him except overcoming them. And that's how he got two powers, Amaterasu and Enton (Amaterasu manipulation)
The situation where he used Genjutsu on KillerBee wasn't difficult for him to dodge since he got a Sharingan which can anticipate moves and can be avoided.
He never used Genjutsu in the future and he awakened Susano'o. Whereas he was spamming Amaterasu and Enton the whole time and awakened Susano'o.
I hope this explains Sasuke doesn't have Tsukuyomi.