I used Mario, Luigi, Falco, and Sonic the most, but top tier has the most obvious changes. I wasn't an expert on the other guys, but these changes are apparent.
ICs: They are gone, but the problem they presented, grab infinites, was globally removed.
Olimar: in Brawl, he could invalidate some characters with his grab, pivot grab, side b, smash attacks alone. His grab had amazing range with low cooldown, and his Usmash and Fsmash followed suit. With red and purple pikmin, he wasn't short on KO power, and with blues and yellows, throws were extra painful and he could have massive disjoints on his moves. Side B was a fast projectile move that tacked on % easily, and required the opponent to attack to remove the pikmin, which Olimar could then punish. On the downside, his recovery was a tether, extremely easily gimped.
In Smash 4, his grab, pivot grab and smashes all have more cooldown making them more easily punished. His maximum Pikmin group is 3, inherently limiting his capability to outcamp characters with side B. His up B was revamped into the winged pikmin, giving him a much more reliable recovery.
Diddy: with a banana in hand and one on the ground, it was nearly impossible to approach this character safely in Brawl. Smash 4 reduced his banana limit to 1, made it disappear on hit (removing his banana locks), removed its transcendent priority, and made it disappear after two throws.
Marth: in Brawl, he could invalidate characters with his fair alone. In smash 4, most of his moveset was slowed down to compensate for the range he has on most of the cast. He can't mindlessly wall anymore to keep characters out.
Falco: Smash 4 nerfed his lasers into the ground, because they realized how powerful a fullscreen, transcendent, auto cancelling projectile was. His Dthrow CG was removed. His near instant Dair was slowed down. His jab 1 and 2 were slowed down and given more endlag so that his boxing game wouldn't be so ridiculous. His phantasm was also nerfed so that his instant air one wouldn't be near lagless.
Mario: Bottom tier in brawl, but helped immensely by hitstun mechanic changes. His FLUDD was buffed by being made transcendent, meaning that characters can no longer attack the water to mitigate the push. He Usmash was also made a bit more reliable for getting KOs.
Sonic: his biggest problem in brawl was lack of reliable KO options. Smash 4 fixed this by giving him two throws that KO reliably, and now the character is a top 10 contender.
Luigi: had huge difficulty approaching in Brawl. He is helped immensely from projectiles being slowed down and given more lag across the board. His cyclone hits were made more reliable and given more KO power, and his fireball is faster to help him deal with projectile spam.
Yoshi: The character can jump out of shield in SSB4, something he couldn't do in any other smash game sans PM.
Ness: a big one that jumps out is that his PK Thunder is invulnerable right after he fires it, making gimping him much more difficult.
There's more, but that should get the gist across.