Anyone who has actively played both RBGs and arenas at the highest level would agree its much more fun and satisfying to win a hard fought RBG with two amazing teams than to win any arena match, but nowadays that is INCREDIBLY hard to come by, it may not even exist anymore.
I don't care to argue which setting has a higher skill cap. But you can't make a demonstrable claim about how "anyone would agree that RBG's are more fun or satisfying". There is no way to prove that the claim is true. People enjoy different game types for different reasons to varying degrees.
Based on my experience as a healer, there are more instances for offensive plays in arena than in battlegrounds (from the perspective of a priest and shaman). In battlegrounds, I am delegated to the role of healbot, spamming heals to the focus target and dispelling other healers as quickly as possible (or other important debuffs on dps). While you still will go for offensive plays in battlegrounds as a healer, it's generally not as consistent or effective, and battlegrounds are not as fun to me as a result.
I have limited experience in rbgs as dps, but I think the same scenario is often true. Dps typically use less of their toolkit to generate a kill in rbgs. Kills are often achieved by coordinated burst by the whole team on one target rather than extensive cc rotations. This should be evident through watching any high rated rbg play - the majority of the communication consists of "everyone go x," not calls of "i'm cc'ing off that." Of course dps are still using cc in rbgs, but again it's generally not as consistent or effective.
You can see an example of my point in this mage vid:
How often is the mage using spells like polymorph in this rbg versus how he plays in arena. He's mostly just spamming damage the entire time. Again, I'm not arguing which setting has a higher skill cap. But it should show that gameplay in battlegrounds and arena is inherently different, and why players might find one setting more fun or satisfying.