I've realized recently that Agatha is among my favorite characters in Pokemon. Besides the fact that her ace is also one of my favorite Pokemon, she's a really fun character in her own right. Her dialogue (at least in the three mainline games she appears in; Bulbapedia doesn't have quotes from Masters) paints her as a skilled battler with decades of experience, and a sly pseudo-mentor who treats her league battles as chances to test young challengers. Her history with Oak is also pretty interesting, as it gives her a connection to the rest of the world that Elite 4 members often lack, and it further characterizes her as someone who puts high value in competitive edge and battle prowess, as well as an experienced old lady who probably has a lot of cool stories to tell (kinda like my grandfather, who had wonderful stories of world travel and advertising). Also, compared to the other members of the Indigo League, her dialogue sounds like something an actual person would say outside of exaggerated trash talk.
Lorelei: "I am a master of ice! Prepare to be frozen solid!"
Bruno: "Me and my posse are gym bros and/or Dragon Ball characters! Prepare to lose to our superior might!"
Lance: "Yo, dragons are fucking awesome! Prepare to lose!"
Agatha: "I heard Oak has been teaching you how to play Pokemon. Bah! That old duff used to be a hunk, but then he became a nerd and went soft. Let me teach you how to
really play Pokemon!"
Two more things to note about her dialogue.
1) Duff is an old slang word for butt, which makes her nickname for Oak ("that old duff") ten times funnier.
2) While the other three express anger and disbelief over being defeated, Agatha's just thrilled that you've got the sauce.
Dialogue isn't the only thing she has going for her, though. Her visual design is also great.
Her more realistic design that she uses in FRLG, Masters, and the show is simple, but effective. Her smirk and glare are pretty standard anime fare, but in this specific context, they mesh perfectly with her dialogue to further characterize her as a crafty old witch who gives you a feeling like she's secretly testing your character, but you have no idea what her tests actually are even though you seem to be passing. I like to imagine that she does this constantly, and only ever makes it obvious what she's testing when she battles someone. Like, you'd catch her staring at you with that same expression at the grocery store or something, and start trying to figure out what you did to impress this witch when all you were doing was buying pasta and cranberry juice.
As great as her realistic design is, I tend to prefer the exaggeration afforded by cartoonish art styles. Thankfully, her more cartoonish depiction in Let's Go and Pokemon Adventures delivers. Giving Agatha a hunch and trading her smirk for a toothy grin really plays up her craftiness and witchiness (and also makes her look like a Gengar). Everything I said in the previous paragraph still applies, but now it feels even creepier when you see her in the grocery store. Also apparently the Kanto Elite 4 is evil in Adventures? Sure, I'll take it. I do love me a scheming villain, and she was already giving me Palpatine vibes.
One more bit of Agatha being awesome: her depiction in Pokemon Generations.
Agatha tests Blue by mockingly comparing him to Professor Oak, and when Blue get mad at the comparison (as opposed to her mocking Professor Oak), she gets excited. Blue passed her test with flying colors. He's got the sauce.