for the falco: the knee made a lot of good points, but i can add a few things. SHL more while he's on the board, not just once you've knocked him off. Fox will overwhelm you w/his speed if you don't. Be careful about using the SHL once he's off the ledge-- you could catch him off guard and he'll fall to his death, but you could also give him a chance to get back on where he may have died otherwise. After a shine, work on WDing under your opponent as opposed to always jumping up after him. These were platform levels, so it makes sense to jc the shine, but levels like FD, wavedashing out of the sine will make your Falco much faster.
for the fox: Make sure you DI. You could have escaped some of the combos faster if you had been DI-ing. Fox can chaingrab Falco, so grab more and do a few jc'ed grabs. I'll have more later.