They are all awesome, and you're making me choose just one?
I will describe what I like about each one:
Falkner: Level 9 Pidgeotto. Awesome blue hair=epic win. Also, not a rock type gym leader. He stands out. (It's a good thing.)
Bugsy: Best gym badge. It's cute, isn't it? I give him props for having a Bug Type gym. (When I first played Gold, I thought Scyther was Johto Pokemon not a Kanto Pokemon. Gold was the first Pokemon game I've ever played/knew about.) I also like Azalea. :) Also, I love his purple hair.
Whitney: Her Miltank is a tough cookie. It's a good challenge. I love the pink hair. She's also a sweet person. I felt bad that she cried.
Morty: He's cool, and his Pokemon can be tough at times. He's a good battler. I'm also a fan of the town he lives in.
Chuck: For a guy with only two Pokemon, he's pretty good. He's the reason why I chose Poliwrath as my water type. (He also reminds me of Chuck Norris. XD)
Jasmine: I love her hair. (I'm so happy she made a cameo in DPPt.) I love her dress as well. Her Steelix is hard to beat if you started off with a Chikorita. When I first played Gold, I thought she was a red head. I liked the overworld sprite.
Pryce: For a guy that age, and still battling, I give him props. He has pretty cool Pokemon. I love the Pokemon in his gym. I love his Dewgong. ^_^
Clair: Her hair is so cool. I love her Pokemon. Especially Kingdra. I loved battling a Dragon type gym leader. I also like how she made you do that extra errand to earn your badge. She made sure you went into that Dragon Den. I probably wouldn't have gone there if it wasn't for her. I also like the fact that she's related to Lance of the Elite Four. She has the 2nd best gym badge. And she lives in one of the coolest towns/cities. :D
If I had to choose, I would say Clair. (Because that's who I wrote the most about.)