They mean the same, but I'm stuffed is to emphasize how full you are.

There are other meanings of 'I'm stuffed', but in general it is just a superlative of I'm full. You can also use a long list of synonyms or superlatives for that, it's pretty common. I'm full to bursting. I'm done I'm stuffed to the gills. I'm tapping out. I'm bursting. I'm plump full to bursting. I'm full up to here. I'm sated. I'm overstuffed. I'm chock-full (to bursting). I'm running over. There's probably a mittful more.

The meaning is the same.