It is interesting to note how, in both Harry Potter and the Sorcerer's Stone and in Alice in Wonderland, there always is a strong connection with the real world. In Harry Potter and the Sorcerer's Stone, beyond the fantasy and supernatural events that abound throughout the book, the reader cannot help to see the usual social relations that are born in a secondary school or a high school, between the different students there. Despite the fact that they study at magic school, inherent issues, like dealing with the class bully or doing homework, are always present. Similarly, Alice is also an early teenager struggling with some of the problems of that age: growing too big, meeting new people and learning to deal with them, tackling new situations that arise in her life etc.

This is similar with many of the characters in both books. Although fantastic characters, they retain many of the usual human characteristics. Dumbledore is, of course, a powerful wizard, but he is also, at the same time, a wise teacher, knowing when to punish and when to encourage. Characters like the queen, from Chapter 8 of Alice in Wonderland, is just like any irrational dictator or boss, in fact. The supernatural beings are all reunited in their overarching humanity.

In fact, L. Carroll draws on many of the characters of his time to paint realistic portraits for many of the characters in his own book. Some are clear allusions to politicians or well-known figures of his day, which is not something that happens in Harry Potter and the Philosopher's Stone, although we do recognize...

Despite the fact that she returns at the same point from the beginning of the book (the river bank and her sister), she has gone, in the fantasy land, through a series of experiences that will improve her as a human being and individual.
Similarly, Harry goes through a continuous transformation, starting from the part where he assumes his magic inheritance and going through all the challenges he needs to pass through in order to become a successful accomplished teenager and wizard. For both Alice and Harry, the events they go through are part of a transformational journey that will make them become accomplished individuals.

Overall, one can probably argue that the presence of fantasy is more emphasized in Harry Potter and the Philosopher's Stone, especially given the fact that most objects tend to gain supernaturals powers, including the usual array of brooms that fly and magic. Alice in Wonderland is certainly much more subtle in alluding to fantasy and in encouraging the reader to use his own imagination without painting a distinct picture of the fantastic events and characters.

Both books, however, are dominated by fantasy and magic and, from this perspective, it is safe to include them in the fantasy genre, despite the different approaches towards this that the authors use.