Both have positives.
Jericho was one of my favorite wrestlers in WCW in 1998. A lot of people looked forward to seeing the nWo, Sting, DDP, and later on, Goldberg (I did as well), but I first and foremost looked forward to seeing Jericho. His change from the good guy face that gave high fives to the crowd and screamed "C'MON, BAAAABBBBYYY" as he walked down to the ring to becoming the loud and braggadocios heel that would collect souvenirs of all of the wrestlers he beat (plus other great things like the 1,004 wrestling holds, etc.) was a pleasant surprise for me. Unfortunately, WCW never got behind him, and he just floundered in the mid-card.
I was not a fan of HHH until DX formed, but as time went on, he began to grab my attention. I still looked forward to seeing Austin, Rock, Vince, Taker, Foley over him, but he was a big part as well. That ladder match with The Rock at SummerSlam 98 is still
. I always thought Hunter would be a mid-carder but it was clear by 1999 that he was going to get in the main event scene, and he did just that later in the year. I think if I had a GOAT Wrestling Match list that his street fight with Cactus Jack would appear somewhere on there and his fed with The Rock is one of the greatest wrestling feuds ever.
Jericho's ability to be versatile and come back each and every time with a new character that works is to be admired and he's had some great feuds and matches with HHH, HBK, Kevin Owens, Cena, Christian, etc. etc. His feud with HBK in 2008 is the only thing that kept me watching during that "Meh" period. HHH is mostly had the same character since....well....forever. We know he's shacked up with the boss's daughter. We know he's accomplished a lot (some through with questionable circumstances). He is The Game. The Cerebral Assassin, Blah, blah, blah. That doesn't take away from the fact that he's been featured in a lot of great stuff too. Some of his matches with HBK, Austin, Rock, Benoit, Jericho, and Batista have all been phenomenal. He managed to get what I think is a 3 star match out of Kevin Nash in a HIAC match. I actually think that match is pretty underrated. He also was shoved down our throat every week, and I have to admit that there was a period in 2002/2003/2004 where I didn't watch RAW because it was basically the HHH show.
On the mic? I'd give this to Jericho easily. Once again, his versatility gets in there. I liked his 2008 calm, cold dimeanor, but I think those times where he would come out and not say anything at all was pretty funny too. Also: "YOU JUST MADE THE LIST!!!!" Although some of HHH's promo's have stuck out. I remember his promo about Flair being a sick dog that needed to be put out of his misery and his promos with Cena leading up to WM22 and his promos with Bryan as well. He's just kind of one note though.
It's really a tough call. I'd probably give it to Jericho, but HHH isn't a slouch and shouldn't be overlooked either. There's a lot of great arguments for him in here as well. Great thread.