I could go into all of what makes fox better than falco, but I don't have time.

Bottom line:
Fox has better matchups across the board than falco.
IMO:
Fox has three even matchups - marth, falco, and an expert tech chasing sheik (fox mirror too but that's obvious) - he beats everyone else.
Falco has six even matchups...again, in my opinion - marth, fox, peach, jiggs, ice climbers, and an expert tech chasing sheik (falco mirror too, but again that is obvious) - he beats everyone else
I believe you can main one of these characters exclusively and win an entire tournament based on that one character. However, I feel like with fox, you have the ability to minimize "adversity." For example, I feel like falco vs floaties
can be tough on the bird if not handled correctly, although PPMD seems to have a pretty good grasp on the matchups.
As the great CeeLaw said above, I feel like falco has more "swag" combos.

However, fox is the character that has the least "disadvantageous" matchups. Personally, I always felt like falco fit my style better. That being said, it really boils down to personal preference.
I wanted to make one last point: I believe that fox, falco, marth, and sheik are elite characters. You can main one of any of them and win a national. Don't forget that you can also get far with peach (armada), pika (axe), cf (the old hax), iceys (wobbles and just recently chudat at Evo), samus (plup - although he mains sheik now for the most part... and hugs)...yoshi and doc (amsa and the old shroomed respectively), and jiggs (hungrybox constantly placing high at internationals - a "god" in his own right.) I feel like we are reaching a meta where we have "viable" characters and characters that are "not viable." You should focus on the handful of characters that are viable, although I would love to see luigi and ness pushed further.
Sorry for the extra **** haha...just rambling. That is my two cents.