When working, there is always the question what you sell? Is it your hours, your time, or is it something else that I deliver.
The major benefit of selling hours is security:: your payment is not 100% linked to project success, – external project disruptions does not affect payment. A bad bug, or bad day, does not cost you anything.
It is easier to relate to, ie. the customer has experience what it means to put hours into a project, whereas they might not know what it is like to build a software project
The benefits of selling solutions is freedom. You own your own time, and it is up to you how to spend it. When you focus and are highly efficient it benefits you more.
I prefer selling solutions. I prefer freedom, also if it means higher risk.