It would be better in the same way that a rainforest is better than a city, which is to say it depends. Basically it would be different, whether it's better or not depends on what you want. I know some people who'd way rather live in a city than a rainforest, and some people who prefer the forest.
In the short term humans have done a lot of damage to a lot of species on this planet (and a lot of benefit to others, looking at you, corn). In the long run, I think there are plenty of disasters that are only going to be possible to avoid through human technological advancement. The increase in sun power mentioned earlier is one, more asteroids or cosmic radiation are others.
Basically, we can have a planet without humans where all sorts of diverse plants and animals live (and still brutally kill each other or die from the environment), but is vulnerable to extinction from giant disasters. The alternative is a planet with humans that has less diversity, lots of urbanization and environmental destruction, but has a chance at fighting back against giant disasters that threaten the entire planet and saving what's left. Neither is necessarily "better", but they are different.
I think the optimal solution is for humans to mostly leave the planet and colonize lifeless places where destroying them doesn't really matter. Let some humans stay on Earth, and basically treat it like a nature reserve. Something to be protected, not exploited.