What's more annoying a flamer or a feeder?

Both are annoying but if I had to decide I would rather take the flamer over the feeder. You can mute the flamer but you can't really prevent the feeder from ruining the game.

A flamer don't cost you games as often.

Definitely a flamer. A feeder loses value the more he dies and often times can be used as a target (people never ignore the 0/8 Ashe even when a 12/0 Akali is bashing their face in) to distract from more valuable players. When you carry a feeder they're usually thankful (unless they were inting) and you score some honor. When I get some toxic manchild in my game flaming his support/jungler/toplane, as though the more he flames the better that player will be, I feel like losing the game just so that guy loses LP. I know I can carry myself in the next game, but I don't want to carry a douche.

feeder. the mute button exists. use it. You can't mute your teammate into stopping feeding.

They are usually both