Do you get a better design with a paid service?
There are 2 options for designing a website, do it yourself, or have someone do it for you. If you do it yourself, I assume you’ll do it through a website building service, using their editor. If you have someone else do it for you, I assume you will have a professional design it.
Based on these assumptions, it depends on which option you choose as to whether your money will have an effect on the aesthetics of your website.
If you do it yourself, you can expect a similar outcome regarding design on a paid version and a free version of a service. It is the templates and design features which will dictate the look of your website, and in a lot of cases, whether your account is free or not, you still get access to all of the templates, and also you are not limited when it comes to design features.
If you pay someone to do it for you, you can expect a better outcome if you pay more. It is much more likely that if you pick a better designer then you will have to pay more than for a worse designer. And if you use a better designer, it’s likely that the design will be better.
If you aren’t very confident with website designing, I still recommend giving a DIY service a go, as the editors are so easy to use nowadays and there are so many templates to choose from, you will be surprised at how easy it is to make a good looking website.