My best guess (and it's nothing more than that, I admit) is that not much happens beyond what normally would happen when swords collide (which is still a pretty amazing mental image when you consider Mech-scale swords!). A vibroblade hitting armor cuts through it thanks to velocity, mass, and the vibration of the blade, but the blade itself is made of much tougher stuff than normal armor would be- so they'd likely cancel out, the same way a normal sword does against its opposite number. Unless one blade has prior damage, or a major flaw, I wouldn't think one would cut through the other, at least not on the first few hits.
Then again, as I said, that's a guess, I'm not a physicist, and Battlemechs remain solidly in the realm of fiction. xp