When should you pick event sourcing instead of regular old CRUD, especially for complicated business stuff?

I'm building a new service, and it's got some really detailed business rules. Plus, we absolutely need to track everything that happens. Usually, we just make services that save data directly, but I've been looking into Event Sourcing. It seems like it could be perfect for us, especially for going back in time to see how things were and for figuring out bugs. My biggest worry is how much more complicated it might make things, like with how we read the data and dealing with data that isn't always up-to-the-second. So, for anyone who's actually used Event Sourcing live, when did you feel like it was worth all the extra work compared to the old way? Are there certain projects where it's awesome, or when it just makes everything worse? What's the main thing you look for before deciding to go for it?