I'd have to say Lance overall although other members such as Koga, Bruno, and Drake come in a close second. Reason why I prefer Lance more though is because of the alpha male vibe he gives off and is one of the few members of the E4 I've faced that's been so challenging yet such a blast to face back then lol.
I like Marhsal, mainly because of his design. Actually, that's all I like about him.
I think my favorite would be Flint. He represents an awesome type and his 'fro will win you over. Eventually. And I think he has a lot of potential to be a deep character, but it's a shame Pokemon didn't want to go into it. I wish he had his own game or something. Anyway, I also like his relationship with Volkner, especially their rivalry.
My favourite's Bruno. Overall, I just really like his character and think it's pretty awesome he's an elite four member in two different games. Flint is also an honourable mention because of dat fro, and speaking of fros...
my favorite will probably always be lorelei...for no other reason than the fact that she characterized what an ELITE trainer would be the very first time you stepped into the elite 4...such a contrast to all the gym leaders you faced up to that point. also, water and ice are awesome
I regret that we don't know a lot of things about E4 members, they all seem to be interesting characters...
Anyway, my favourite E4 member is Lorelei. Because, being the first E4 member I ever challenged, the feeling I felt when I saw her the first time is so unique... I don't know if it's the same in the english version, but in the french one Lorelei lisps, and that adds her something different than any other characters. That adds to her something funny and original.