What is more important for the web site? Consider that for a moment. You can control your own web site, its pages, its content etc but you cannot control what happens outside of that; who links to who or what. What do you think is more important? You can change things on-site, you can tweak paragraphs and image attributes. That sounds quite important. You can reword a web page Title. That's important shit in SEO. Johnny Twofacefingers in Brazil may or may not link to your web page. Is that important? Does that sound earth shattering to you? Who cares!
On-Page and OFF-page SEO both are most important for your website.
For ranking point of view; on-page optimization factors are more important for your website. For doing on-page, first you need to define keywords for implementing website & its service pages or subpages. Here are most important to things that, which types of keywords you choose. If you choose "low search volume keyword" and also with "low competition" for that keyword, I think website doesn't need to do Off-page optimization. Or if you choose high/medium Search Volume and high/medium Competition keywords, you should go for off-page optimization. So here must require off-page optimization for website SEO.
Search engine optimization (SEO) is the process of affecting the visibility of a website or a web page in a web search engine's unpaid results—often referred to as "natural", "organic", or "earned" results.