Triforce will do more for Udyr against squishies, whereas Black Cleaver will only be really useful against tankier opponents.
Udyr can proc the spell blade on Triforce every time it is up, giving the overall damage edge to Triforce. If Udyr is looking more to support his allies, BC will be okay, the tiger stance will be very effective with it's tick damage on top of the armor reduction from BC. It also gives CDR, which is good for Udyr, he could skip Frozen Heart if he wanted Randuin's for more effective health.
I think I agree with everyone in that it would be highly situational which one you take, if you take either one at all. Udyr is so well designed in that he can do well with almost every item in the game, so either item will most likely be effective on him in some way, but there will be a trade off and a benefit to using each of them.