On the most basic level, Salem's House is a pretty awful school while Dr. Strong's school is a fine school.
Salem's House essentially treats its pupils like inmates at a prison. The master takes pleasure in using corporal punishment on the students, not because he thinks it will make them better people, but because he relishes the power he has over them. As the other answer mentions, the very building and its rooms are poorly maintained and dreary.
That Mr. Murdstone sends David to this school is telling. The school reflects Murdstone's cruelty and uncharitable view of David's character. He does not believe in nurturing children so much as ensuring their blind submission through any means necessary.
In contrast, the Canterbury school treats its students with respect and does not assume they are evil little beings who need to have proper education beaten into them. It is assumed that students are at heart not bad people and this inspires the students to do their best generally. The building itself is neat, clean, and dignified.
Dr. Strong himself is an honorable, reliable man and he inspires his students to cultivate these qualities in themselves. He is the good father figure to the tyrannical models represented by Murdstone and Mr. Creakle.
Salem House "was a square brick building with wings; of a bare and unfurnished appearance", and its rooms have a "strange, unwholesome smell". Salem House (note the name, and its reference to the devil!) is run by the monstrous Mr. Creakle, who seems to take a perversely extreme delight in thrashing his pupils. Worryingly, Dickens' portrayal of this monstrous teacher was seen as an accurate satire of certain contemporary schoolmasters.
Dr. Strong's school in Canterbury is its opposite. Pupils are assumed to be honorable, intelligent, well-meaning, and are treated extremely kindly.
Dickens makes the difference very clear in Chapter 16:
Doctor Strong's was an excellent school; as different from Mr. Creakle's as good is from evil. It was very gravely and decorously ordered, and on a sound system; with an appeal, in everything, to the honour and good faith of the boys, and an avowed intention to rely on their possession of those qualities unless they proved themselves unworthy of it, which worked wonders.