A lot of players aren't comfortable playing "clunky" heavyweights, which I think hurts Charizard's usage somewhat. That said, he can be a very rewarding character to master because of his incredible speed, power, weight and recovery and has his own niche in the Trainer's team.
As for individual character strengths I'd say that they go like this:
Squirtle - Evasion and combos.
His small body and great air acceleration make him great at avoiding enemy attacks while his frame data and low power makes him great at stringing together combos. Should mostly be used when he and his opponent are at mid to low percents as he is seriously lacking in weight and killpower.
Ivysaur - Range and defensive play.
Ivy is the best when on the defensive of the three as he (or she if you prefer) has a great projectile and solid disjoints. Although they struggle playing aggressively, getting out if disadvantage and recovering Ivysaur is easily the most flexible of the three thanks to a great neutral game and solid kill options but is generally best at mid percents.
Charizard - Speed, power and survivability.
Charizard is combo food and is an easy target and as such shouldn't be used at low percents, but has a plethora of killing options and a much better weight and recovery then Ivysaur to continue living at high percents. I think of Charizard as a momentum character who can their survivability and powerful advantage state to create huge leads after a kill when played right. Obviously best to use at high percents but is good enough at racking up damage to be used no matter what percent your opponent is at.
I generally don't get as many chances to play Zard against opponents who are good at killing but against those who do he can be an absolute monster. He's also even better at killing then Ivysaur so he's useful when fighting enemies who are hard to nail with Ivy's uair.