Chris Winkle compiled a list of successful companions and their common traits. He said,
“If the animal is small, they can easily tag along and participate in fights without solving the hero’s problems for them. As long as they help out, it’s okay if they cause trouble or need rescuing occasionally. A good animal companion has a distinctive personality that plays well with the hero and creates fun or touching scenes for the audience to enjoy.”
Small likely means that the companion can be utilized more frequently. They can sit on the main character's shoulder like Pikachu (Pokemon) or on their head like Pascal (Disney's Rapunzel). They can even be tucked away like Navi (Zelda: Ocarina of Time), or Baby Yoda (The Mandalorian) in his hover pram.
There is always a risk that writers will underutilize large companions, which means they won't get as many opportunities to fulfill the rest of Chris Winkle's criteria for successful companions. Lion (Steven Universe) is used infrequently despite a lot of effort to give him a distinctive personality and meaning in the series. In an Our Opinions Are Correct Podcast, Lion is mentioned in passing. They argue that Lion is a metaphor for Steven and serves as a connection to his dead mother. Lion also foreshadows the big reveal at the end of the series. The Stark Direwolves (A Game of Thrones) are underutilized particularly in the tv series likely because they are easier to manipulate on paper than on screen.
To get around this, many stories where large companions are used successfully, center the plot around the size or use it for comedic effect. The plot may even feature difficulties hiding the companion. Prominent examples are Baymax (Big Hero 6), the Iron Giant, or Charlie (Sweep: A Girl and Her Monster.)
Other times, large companions are given special properties to make them appear and reappear or exist as a voice when the body can't be present. Some examples are TARS (Interstellar) who communicates with Cooper over intercoms, My Board (Silver Surfer: Anywhere and Everywhere) who is part of the Silver Surfer and has a mind of its own, and the Stark Direwolves (A Game of Thrones), who can act as surrogate bodies for the Stark children.
Small companions are also "underpowered." There is room for small things to grow, to succeed despite terrible odds, and also to fail.
"Be a sadist. No matter how sweet and innocent your leading characters, make awful things happen to them—in order that the reader may see what they are made of."
Large companions need additional flaws that hold them back. Lion (Steven Universe) is quite powerful at face value, but he has one feature that gives Steven some wiggle room to solve problems in his way. Lion is lazy. Baymax (Big Hero Six) is programmed as a Healthcare Companion; not a superhero. The Iron Giant is unaware of his power and acts as a curious child.