The winner of a Goku vs. Ryu fight has never been explored officially, although there are many fan-made battles on YouTube and online forums. According to Dragonball.wikia.com, judging by his powers and adventures, Goku would almost certainly win such a fight.
The major difference between Goku and Ryu concerns their enemies and battles. Goku fights planetary threats and alien super-beings, whereas Ryu enters martial arts tournaments against other humans and enhanced humans. Furthermore, Goku has the ability to level up his powers interminably, reaching godlike forms known as "Super-Saiyan." Additionally, there are multiple tiers to the "Super-Saiyan" level, which further makes a battle with Ryu look very lopsided.