They're both just as famous as each other
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Personally, I don't think either of them are more famous than the other
Jabba the Hutt had several pets. If you are talking about the monkey-creature that sits on his dais his name was Salacious Crumb. If you meant the beast that Luke fought in the pit than that was the rancor. There is also the frog-creature on the stair named Bubo and often the hutt's slave girls are considered as "pets". If none of these answered your question be more specific.
Garfield
Sadly, Garfield (a cartoon cat!) is more widely recognized.
Mario has been around longer than garfield and has always been more popular by far.