As great as the Sly games are, Star Fox will always be the better series to me, I used to play Star Fox Assault for HOURS on end when I was 10. As for who would win in a fight I am not sure, It is pretty damn even. For that reason I will just side with my innate bias and say that Fox takes it 6/10.
Fox, hes fast and quick and more then likely being a mercenary the whole Starfox team(with maybe the exception of Slippy) have been trained in H2H combat. While not shown, it would be kinda both dumb and not very professional like if the mercs can't handle themselves without a blaster...though it was kinda shown in Adventures with Fox wielding Krystal's staff that could support that all the members have been cross trained in various fields of combat.
Also going by nature, Foxes hunt Raccoons...just throwing that out there.