I'm a consultant too and hourly has many problems as well.
The core issue with hourly is it means you earn less if you work faster and smarter. This disincentive is very bad for you and the client.
Also, the client is going to hold you to your estimate anyway and once you start getting close to it you're both going to get stressed and not do your best work. The client will start securitising your time sheets, you'll start eating hours to avoid angering the client, and you'll both waste hours every week on timesheets and billing. That's all time you're not putting into the project.
I'm not saying fixed price is always the best option but I prefer them. The only time I've been burned by them was when I wasn't the one deciding the fixed price. If you're suffering from scope creep and bad estimates, there's ways to fix that.