IMO, conkeldurr fears skarmory much more than breloom does. Skarmory outspeeds conkeldurr and taunts him before he can get enough boosts. Breloom is usually able to outspeed skarmory and put him to sleep before he can threaten breloom (assuming sleep clause isn't already active), and therefore fears him much less. Also, breloom can boost its attack TWO stages in one turn thanks to swords dance, something conkeldurr can't do.
Dude I think your completely off. First of all I was talking about Sub Punch Conkeldurr so taunt really doesn't bother Conkeldurr that much. If anything, SubPunch Conkeldurr has an easier time with Taunt Skarm because they usually drop Brave Bird for Taunt...
Now Breloom fears Skarm way more than Conkeldurr does. Like The Truth said, any decent player would bait a spore and save Skarm if they were facing a Breloom. Breloom cant set up on skarm because its 4x weak to Brave Bird and Sub Punch can't hit Skarm as hard either. Conkeldurr on the other hand can easily take a Brave Bird if needed and has a chance to 2HKO with SR.
IMO Conkeldurr and Breloom are very different pokes that are played completely different from each other. Don't know why theres so much comparison between the two.