For me this is a difficult choice because I love both Arcanine and Houndoom for many reasons. I also love Growlithe and Houndour the same. I love canine like pokemon, and in generation one I always had Growlithe (well once you could obtain it) and Arcanine on my team. Basically, Arcanine is such a beautiful pokemon, it's mane really tends to flow gracefully and it just captures you with it's stunning beauty. I love how awesome it always looked to me in the game, on the anime and on the cards. I also found it to be quite powerful in battle for me and was ultimately my favorite fire type back then besides Charizard.
But, Houndoom just looks so bad and like it can cause you to shudder. I have always been a fan of it's design as well, it just looks so cool yet deadly. Love the horns and the tail, and it's just so unique to me that I can't discredit it. Once generation two came along, I was also persistent on always having Houndour or Houndoom on my team because I also just loved the fact that it was also a dark pokemon and not just fire.
For this, I'm afraid I have to go with Houndoom because it's been on my team more after generation two, mainly because it's also a dark pokemon. It's look is also cool yet it looks fierce and I like that. However, If I were to choose over design, I'd probably say Arcanine because it looks like it's legendary and epic.