Is there a big difference between the two breeds over all?
Cochins have single combs and feathered legs.
Wyandottes have rose combs and clean legs.
Or at least, Wyandottes are SUPPOSED to have rose combs. Sometimes they produce chicks with single combs, which only matters if you care about the comb type. If you want to enter them in a show, the comb type matters. In many other situations it does not matter.
Body shape and size should be a bit different.
I would expect Wyandottes to mature faster and lay more eggs. I would expect Cochins to mature later (bigger birds so they spend more time growing), and lay fewer eggs (fewer per week, plus a later start.)
For maturity and egg laying abilities, where you get them can make a big difference. Different sources are focused on different traits-- that could be two different hatcheries, or two different private breeders, or one of each. If you got both breeds from several sources, you might find that the earliest and latest layers, or the best and worst layers, were the same breed from different sources, with the other breed being in the middle (no, I can't predict which breed would be the outlier or the one in the middle. That is just an example of the kind of thing that can happen.)
I was leaning towards cochin as they are heavier and I may not have to tip their wing to keep them from going over the fence when free roaming. But noise level and friendliness are factors I am looking into as well.
Unfortunately, I can't help with any of those specific points (although I do see that several other people talked about them.)