Its easier if you just run on the idea that Bugs and Daffy and Kermit the Frog are actors, and this is just one of many roles in their 60 year career, as opposed to being a genuine insight into their real lives.
With that mindset, its okay that the tone or feel or look of it are different. Robin Williams isn't the same in every role he plays, and he switches up genres and his appearance all the time. Sometimes its comedy, sometimes its serious, sometimes it with a beard and sometimes without. Its an actor thing.
I was actually pretty amused by Daffy's rapily escalating lies, in a fairly short clip.
"Are you saying the president of Mexico… is Batman?"
Anyway, here's a modern classic from all the way back in 1995.
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Interesting in that they had to use Penelope, due to lack of female Looney Tunes. if it had bene made a couple years later, it'd no doubt be Lola in the role instead.