Hmm this is a good interesting one. Well at first I was like this is difficult to answer, but then I remember having my blog. I think it is pretty faster to get traffic with blogs, because You can write the contents by yourself, so you can write as much content as possible and get picked up by search engines, but for forums, you have to get users to sign up and add content which will help the site pick up. So it could be slower for forums to pick up traffic than a blog.
In fact, I think the question should be which is easier to pick up traffic in the beginning. Blog or Forum?
because some forums that already popular today get more traffic than unpopular blogs and vice versa.
There's no straight answer to this question. These are two different types of platforms and are meant to serve completely different purposes.
Speaking of traffic -
If you're looking for organic sources, blogs are way ahead of forums because usually blog posts are better optimised for search engines than forum threads.
Blogs enjoy better traffic from social networks too because their content is more suited for sharing on such platforms.
However, with a forum, you can get a lot of direct traffic from the members which mostly doesn't happen with a blog, unless it's an authority blog.
Further explanation -
With a forum, you have little control over the quality of content that's getting published on your website. It's user-driven. If you're successful, you earn a number of loyal members who are willing to spend time on your website and help it grow.
With a blog, you decide what to write. You get to choose your topic, do keyword research and create content. You have everything in control that includes the quality of content.
Blog and forum links are not enough without a good on-page SEO strategy. Also, quality content for both on-page and off-page tasks also matters a lot. I think you should give great importance to guest posts on high traffic sites here.
It's not a function of website type, ie website vs forum that dictates traffic but rather the amount of quality, original, indexable content. Content is king. The more words and pages your website/forum has the more likely to achieve higher Google rankings and drive meaningful traffic.