In my opinion having both is better. In the beginning I only had my laptop but felt the need for a pc for what I wanted to do but I could not afford it. So I decided to get a T-external memory, just in case the laptop died on me. Later on I was able to get a very good pc, but now my laptop is kinda, getting there lol
So it is great that you are backing up all your info; that is always the most important thing as technology unfortunately, sometimes just fails on us. I think getting the external drive was a great investment because not only is my information protected, but also, I can provide better and faster service in my already fast pc.
But definitely having both is best for your business, in my opinion. You can have your work at home computer and if you would like to personalize it more, you take your laptop to a coffee meeting and provide information about your services with a presentation. And you don't have to worry about you information because it is already protect in your external drive. Hope this helps.