Fox in Melee actually looks like a badass. A character that was once a campy stuffed animal on a box became cool. How did they do this? Again, a lot of it comes down to proportions.
The most obvious difference is his head shape. Melee Fox has a longer snout and it takes up more space on his face. It is very close to what you would expect from a matured canine in real life. New Fox's head is more cartoon inspired. He's got a tiny little snout dropped down to the bottom of his face and a massive cranium. This styling (possibly unbeknownst to the artist) makes him look like a baby/much younger animal. He's goofy looking, not cool or imposing. He also has the build of a young boy, maybe pre-teen age. Melee Fox appears to have a more muscular build, wider shoulders, properly fitted clothing (dem shoes). Compare their head to body ratios. New Fox's head is massive, possibly even bigger than it was in Brawl.
It's unfortunate that Fox will look like this for a second time because of a poor redesign. I mean, just look at the old Fox. Dude's just standing there and he looks like he could reclaim a star system without breaking a sweat. Teenfox looks like he's runnin' off to clown college.