I know there seems to be a feud between these two but believe it on not, I've never posted in one of these threads before. I don't even know which show I personally like better. Both shows disappointed me a lot, but I also enjoyed both.
As for evidence, it's not as if anyone is running a reliable poll on which show is more recognized and influential. But at the very least, referring to Adventure Time as>>118646796>just a fart in the wind that was popular for like one summer and then disappeared.
Is stupid, the show ran for 10 seasons and sold plenty of merch for your metric. That's actually how I know about kids and adults having watched AT, I don't ask, I just see people I know or around wearing AT merch like pins, having AT desk figurines, AT pencils, etc. I'm sure part of this is Disney's fault but I have never seen any GF merch.
Most people arguing for GF's influence seem to be arguing that Amphibia and Owl House are just GF ripoffs, and that makes it more influential. The thing is that the small cartoon industry is extremely incestuous, and both Disney tv animation and Cartoon Network just use the same small core group of people over and over again (and to a degree those same people jumping from network to network). So two people from GF work created Amphibia and Owl House. But I would argue that Owl House is more like Little Witch Academia in a lot of ways and I don't think the comparison is uniquely striking. So many genre shows have a dorky kid protagonist, both lore and humor, typical genre fantasy shit, etc. I see a few notable things but not enough for me to call it a GF ripoff when Harry Potter and LWA feel more ripped off from.