The problem I see with this issue is the difference in degrees of power. A good majority of the Channeler's we see in the Wheel of Time books are regarded as some of the most powerful Channeler's with years of experience backing them. In Mistborn, on the other hand, almost all of the Allomancer's we see are on the weak end of the scale, and have had Allomantic training for only a few years.
Compulsion, Balefire, Rey's shield, all of those take a significantly large strength in the One Power to use. If the Channeler in this fight is that strong, then it's only fair to have an equally strong Mistborn. Say, someone along the lines of Elend's or The Lord Ruler's Allomantic abilities, perhaps even a full-blown Mistborn savant.
Now that that's out of the way . . . Weaves of Air.
I'm pretty sure trapping a Mistborn in a weave of air would be the stupidest thing one could do. The reason? Weaves of air keep the target pinned with a (nigh) unbreakable force. This would mean any Steelpush or Ironpull performed while trapped within a weave of air would have an (almost) infinite weight backing. Just like a coin hitting into a building can push back with a lot more force, the Mistborn hitting into the weaves of air would gain pseudo super-weight. Building in your way? Steelpush it flat. Pesky Aes Sedai bothering you? Smash her with an iron boulder or two. Annoyed at life in general? Do a massive ironpull on the planet's metallic core, and watch as waves of molten metal cascade down upon your enemies, heralding the end of life as they know it as their planet collapses in upon itself. (Though I'm pretty sure that one would kill you too.)
Of course, that may be a tad dramatic, as it's much more likely the weaves of air would just break, giving the Channeler a nice little migraine as their weaves snap, and sending the Mistborn flying off who knows where. After all, Channeler's can't just go lifting up mountains with air, and a properly positioned Steelpush would do just that.
If that isn't enough for you, there's always the old argument of the proper application of electrum and atium. Burning those two metals, a Mistborn knows everything that could possibly happen around him, and by focusing on the proper electrum shadow they know just how to turn any situation to their utmost advantage. (Or at least how to stay alive.) Lightning going to strike from the sky? Atium-shadows, or if that doesn't work, stay away from the electrum paths that show you getting fried. Weave of compulsion headed your way? Stay away from the electrum shadows which show you stop moving. (Though that could be a weave of air as well.)
Finally, I would not dismiss zinc and brass so easily. It's true most Channeler's are trained to keep their emotions in check, but I'm not so sure that would hold up if a Soothing or Rioting was fueled by duralumin. I see that as having an effect much like giving up Biochromatic Breath to someone. The shock is essentially unavoidable, and all it takes is one moment out of control for the One Power to drag you under.
Now I'm not saying it would be Mistborn > Channeler in any fight, by no means. But I don't think it would be quite as cut-and-dry as most people make it out to be. It's just all about the balance of power between the two groups. If we're going to have high-strength Channeler's going at it, we need to have high-strength Mistborn as well.