From /u/enuna-baeley-lune since her comment didn't show up her for some reason:

I'm going with Ike all the way for this one. And I say that for another reason entirely other than what I like to think ^{if ya know what I mean wink wink hint hint.} Anyways, the reason I say this is because of the multiple sources of where it's hinted, or blatantly said he really enjoys eating. My first and most effective point would have to be the one support conversation him and Titania have in Path of Radiance, where it's said Ike really enjoys eating/has a really big appetite, and also brought up once again during a conversation with Soren and Aimme. Not to mention this conversation states his favorite things to gorge on would be meats of any kind, especially steak and ribs. This point could be also further hinted throughout other sources like SSB4, where you complete either All-Star or Classic mode with Ike and receive a "Congratulations" picture which features him eyeing a turkey food item. This is probably used to connect to his love for meat exposed in PoR. Adding to that, in the new Fire Emblem Fates game, once you connect the Ike amiibo into the game, his first conversation with Corrin includes him saying that he was offered to be fed by one of his friends, all the while not bothering to bring up any other points like if he was offered shelter or any other sort of help like that. This could also most likely link back to the fact of him having a rather large appetite over anything else. Putting these pieces of evidence together brings me to strongly believe that Ike would win over Inuyasha in a hot dog eating contest. The fact that his voracious appetite is exploited throughout multiple sources, and that he prefers eating meat over anything else also helps his chances in this contest seeing that hotdogs are a meat product themselves. Although in some episodes of the anime, it does show Inuyasha pigging out on a few family meals at Kagome's house, or on a picnic lunch with the others, Rumiko Takahashi never makes it directly apparent that he is a total glutton. With him being a half-demon, giving him super human strength, powers, etc.. could also help with his chances in this contest which could result in him having a more expandable stomach and the ability to eat more. However, anytime he does sit down to have a meal, it never does show his stomach greatly expanding to drastic proportions. I'm not saying it isn't possible for him, but his appetite is just not as perceived or developed compared to Ike's. Although I haven't read the entire manga, I only own book 1 of the Vizbig books, so if there IS anything in the manga depicting his appetite more than the anime, feel free to let me know. Other than that, my money's on Ike.