In general, I use both story points and hours. I also work hard to decouple any kind of comparison between the two. They are two different measures which give two different views into the level of commitment as well as health of the sprint when in progress. (Note: I'm assuming scrum here.) To this end, I move away from using any kind of points-to-hours conversion/comparison chart as soon as possible. Although it is helpful to sometimes start with just such a chart.
Time estimates are familiar to delivery team members and are somewhat easy to quantify - everyone makes estimates for how long something is going to take in many aspects of their lives, not just work assignments. If used in concert with evidence based scheduling, the release cycle can reveal valuable insight into the estimation skills of the team and individuals.
I frame story points as a measure of all the other "stuff" about estimating a work effort: complexity, card dependencies, client dependencies, technical challenge, problem definition, etc. - basically, that immeasurable intuitive feel a team member has based on experience in the industry, with the company, and with the team.
With respect to the Fibonacci scale, I've found it much more useful to have 3-5 points reflect something around an 8-hour-ish effort. When efforts start showing 8, 13, and 21 points, it becomes much more apparent to the individual and the team that a story may need to be broken into smaller tasks. That's the value using something like the Fibonacci scale. It helps shake out planning fallacy bias if used properly.