Before taking off my Nintendo Defense Squad Uniform, I'm going to mention that Star Fox 64 was great.
With that out of the way, it depends on how you qualify the success of Fox and Ratchett: in-universe or in terms of real life game quantity and/or quality? In universe, I would vie for Fox. Before the beginning of the series (SF64 kind of took the SNES original's place in continuity), Fox and a couple of other flight school dropouts teamed up with his dad's elderly friend to become a squad of elite mercenary fighter pilots. He was still a teenager. In 64, he and his three friends singlehandedly turned back an invasion before heading to the enemy base, destroying countless enemies along the way. A typical SF64 run will often net over 1000 kills in an hour of playtime, often more if the player is skilled or chooses a specific path, and bosses include giant mechs, space battleships, fiery elementals on the surface of stars, and eventually ditching his friends because he feels like beating the final boss by himself. Note that he fights using the Arwing in Space and Aerial battles as well as a Tank and Submarine.
He was still 18 years old by the way.
The next game, Adventures, has Fox go to a planet inhabited by giant dinosaur monsters and whatnot... on foot. By himself. Primarily using a magic stick he finds on the planet, as opposed to a laser gun. The game has an early boss where Fox defeats a giant T-Rex by going inside of its mouth and beating the boss's insides to a pulp until it dies. Suffice to say, Fox is a master of non-vehicle combat.
The other two games just carry on the theme. Fox is basically capable of doing any kind of sci-fi space action he comes across, can do it very well, and can do it solo.
Ratchet is by no means unaccomplished. However, he often seems to get more help from allies, especially Clank, than Fox does. He also has far more impressive gear and firepower on foot, which makes some of his feats a bit less impressive in comparison. So I have to give Fox more credit in this sense.
In real life terms though, Ratchett takes the lead. Fox really only had one big game in terms of acclaim and sales, back in 1997. The GameCube and DS games were not badly received, but were not successful enough for us to have gotten a new Star Fox game for nearly a decade. Ratchet, meanwhile, has starred in about one game per years since his 2002 debut, with the original PS2 trio matching SF64's level of acclaim and a few other entries exceeding all other Star Fox games.
