There are a lot of software as a Service (Saas) companies out there who are providing business owners a fantastic user experience for performing billing tasks, expense tracking, and other admin and management functions. These SaaS companies are very far ahead of all full service accounting solutions Quickbooks in their niche but the are not full accounting software.
Most of the SaaS services who say they are accounting software (Outright, Freshbooks, etc.) are just tracking or categorizing your expenses and doing a very basic income statement rather than a set of financial statements that would include a balance sheet (shows the value of your business assets and liabilities). If you were to ever use your business to try and get a loan or a mortgage, the banker is going to want to see this balance sheet.
So, at least for now, as a general rule you should probably have Quickbooks if you are making money already. However, it is possible to build a custom solution if you need help integrating these with your existing system. My guess is that Intuit will likely buy one or two of the these cloud companies in the future instead of trying to make their product user friendly for the small business owner.
Most business owners do not understand Quickbooks but they do want to be able to manage invoices. I spoke with Freshbooks and there is some development activity that will sync the two services organically. For now, we are using a custom Beta product to sync Freshbooks and Quickbooks for our clients.