Seems like what you are asking is should you use a WordPress template to build a site or building a site not using a template.

It all depends on your budget but if budget allows and you are serious about making your site unique and want to avoid the possibility that someone else might be using the same WordPress template, then build a custom site.

You can use WordPress as a CMS tool to build a custom site. Just because you are using WordPress, it does not mean you have to use a pre-made WordPress template. We have designed and built many sites using WordPress as the platform and each site is not built using any templates.