As the title suggests we will talk about Caesar Clown and Buggy the Clown and how actually Caesar’s actions and interactions reminds me of pre-timeskip Buggy.
1. To start with the obvious they both have Clown in their name
2. Both of them were living in the shadow of someone great (Gol D. Roger for Buggy and Dr. Vegapunk for Caesar)
3. Buggy was able to capture Luffy and almost executed him because Luffy was not taking him serious and he was fooling around.
The same thing happened when Luffy first fought Caesar. Caesar caught him off guard and was able to defeat Luffy.
4. Just before getting executed by Buggy, Luffy was saved by Dragon.
When Luffy was tied with prism stone and Smiley was coming in Punk Hazard he was saved by Law good planning, otherwise he was dead.
5. Buggy helped Luffy unwillingly during Impel Down because it was his only way of surviving the wrath of the guards.
Caesar helped Luffy unwillingly during Dressrosa because it was his only way of survival and hoping that way to avoid the wrath of Doffy/Kaido and Big Mom. They also reluctantly formed an alliance to overthrow their shared enemy Big Mom.
6. Both Buggy and Caesar have/had armies following them under false pretense or wrong impression for them.
Buggy is seen as a strong pirate who once was travelling with Roger (the prisoners from Impel Down).
Caesar is seen as a savior (for all the people in Punk Hazard).
7. Both have very similar gag moments and reactions with Luffy, where Luffy is clearly disrespecting them with the nicknames that he is giving them.
*Theory by Capt_NakedPanda