Generally speaking, they are NOT of equal importance in terms of rankings. They each serve a unique purpose.
External links, or those pointing to your website from other websites on the web, impact your search rankings. The quantity, quality and types of links impact how your website is perceived by search engines. They are to be thought of as votes of confidence or signals of trust (this only pertains to white hat, natural links). Gaining external links to your website is a necessary and essential part of ranking your website on the first page of Google and other search engines. It is also important to getting a webpage indexed, though not always necessary.
By contrast, an internal link is a link that is on one of the pages of your website that leads to another page on your website. Linking internally is important to helping users find the information they are looking for; it is also important in creating a page hierarchy that helps Google see which pages are “more” important on your website. The more internal links pointing to a particular webpage, the more important that page may appear to Google. This is a generality. How you code the links, from what pages they come etc. all impact the end result. It’s good SEO practice to link two related pages. For example, if you write a blog about how to grill fish using a rub, you may also link to a page on your site where you sell that grilling Rub. The pages should be related and relevant to the visitor. They should seamlessly connect the user to another part of your website that makes sense.
It is important to remember that in the end, a website is about getting results—that means getting a user to take a desired action. If external links can help bring the horse to water so to speak, then internal links are equally important in getting them to drink i.e. move down the sales funnel from prospect to a lead. If you focus on what is good for your customer, you will most often make the right decision.
If you are not sure what to do or have questions, you can always reach out to us. We are happy to talk to you about your SEO needs.