I caught him, of course, because you sort of feel like you have to. It's one of those things where it's special in that it's not regular-coloured, and there's only one chance to capture it so you feel like if you don't then you've missed out on something. Then once you do catch him you're like "alright... well what now?"
I remember on GSC when the Red Gyarados was such a novelty that everybody used him, but I never did - and here's why: I like my Pokemon's colour to match their type. So I don't like using Water Pokemon that aren't blue, Grass Pokemon that aren't green, Electrics that aren't Yellow/Orange and so on. So following the same principle in the remakes, I caught him and boxed him, and used my regular blue Gyarados on my journey.