With first person, you get to describe events with the character's own words. This can make events feel a lot more personal, like you're actually experiencing them through the character's eyes. This can be really good for introspective stories about a specific character.
On the other hand, third person is more flexible. Since you're not confined to one character's viewpoint, you can describe things that the main character might not notice. You can even look into the thoughts and feelings of specific characters at any time. The one issue being that it can get a bit confusing if you swap between characters too much.
That being said, I don't have a strong preference toward one or the other; I think it depends on the needs of the story. As a writer, though, I usually go for a pseudo-first person, where I write in third person but focus primarily on one character's viewpoint. I find that to be the most flexible while also being the least confusing.