I'm a bit confused by the question because there isn't an official Harry Potter anime, so I'm assuming we're talking about hypothetical fan-made stuff or maybe someone mistaking the new HBO series for being animated? Anyway, if we're imagining a straight adaptation into an anime style, I think the tone would be the hardest thing to nail. The books shift from a whimsical, almost Roald Dahl-esque vibe in the early ones to this grim, politically-charged war story later on. Anime tends to stylize emotions so heavily—you get the huge sparkly eyes for wonder, the exaggerated sweat drops for anxiety, the super-deformed chibi moments for comedy. That could either amplify the charm of the early years beautifully or make the darker moments feel weirdly melodramatic.
What I'd be most interested in, though, is the visual language. An anime could finally do proper justice to the magical creatures and spells in motion. Imagine a Quidditch match animated with the fluid, dynamic camera work of something like 'Haikyuu!!', or the Dementors rendered with the eerie, glitchy horror of Junji Ito's style. The books describe these things, but an anime medium could make them visceral. On the flip side, I worry the internal monologues—so crucial to Harry's angsty isolation in 'Order of the Phoenix'—might get lost unless they used a lot of narration or symbolic imagery, which can be hit or miss.
Honestly, the comparison would likely hinge on pacing. The books are dense with lore and side details. An anime series, with its seasonal structure, could either expand on those wonderfully (filler episodes about life in the Ministry? Yes, please!) or butcher the plot to fit 24-episode arcs. I love the books for their textured world, but an anime might succeed better at pure spectacle and emotional crescendos, maybe at the expense of that cozy, detailed immersion.