As far as difficulty, I never had much trouble with either of them, which really disappointed me. However, if I had to pick one on that front, I did mow over Alder more easily than Iris, so Iris wins that one. She could probably easily mow over his team...then again, she probably had to to take the Champion title from him.
When it comes down to presence, character, and all of that jazz though, I've got to hand it to Alder. I feel like you see him a decent amount of times in BW and even in BW2 when he's no longer the Champion, I still see him as one because of his attitude, the wisdom he instills in your character, and the help he provides to you early on. It's more than I can really say for Iris, who you see a lot in the first games (which is great!), but not enough of in the sequels where she actually is the Champion.
Alder is actually one of my favorite Champions overall though, so I guess it was no surprise I was going to go with him here, haha. Battling isn't everything to me and Alder's character stands out enough from his battle (and even then, I like that it's more of a friendly battle than something super serious like all the others, so that in itself stands out as well) to make him shine as a Champion in other ways.