I'm not saying they suck, just that the Asha'man are better weapons period. A dagger can kill a man, but an ax can cut his damn head off :p

Listing off their resume of battles only strengthens my point. Dumai's Well to start, the Asha'man had to fend off many channelers, which was extremely easy, then turned the army into soup, the rest were so badly demoralized that they through down their weapons and ran. RJ made this point so well that he had to step back and separate the Asha'man so they didn't steal all the "power" spotlight, you also notice the black tower conflict is being held to the very end.
There have been numerous times the Asha'man (always out numbered) face other channeling groups and kick there ass. Illian/Altara battle wasn't involving them either, it was Rand vs the Seanchan.

As to the war dog destroying armies??? What are you smoking, they have shot a few lightning bolts into the battle, but the troops and beasts do most the work, and they haven't really destroy any armies. They have beaten a few countries they were demoralized and filled with hopelessness, so those armies joined them for promises of titles and wealth.

So with the whole Seanchan arsenal of Demane/beasts/troops they have injured armies until they give up, little death. Asha'man on the other hand slaughter thousands in mere minutes and you say the Damane are better weapons? more effective in destruction? MY ASS.