Well, in short, the archive is something that WordPress generates for the Post Types or taxonomies or authors.
It's a loop of Posts, that is always available under the URL "my-site.com/post-type-slug/" or "my-site.com/taxonomy-slug/taxonomy-term-slug" or similar.
A view, on the other hand, is a List of Posts, that you can insert everywhere you want.
Both can have Custom Searches (meanwhile), but only the View can be inserted everywhere and display it's results on other pages as well. The archive, will always and only be available under the Archive URL, and usually depend on paginations too.
The question is less about a Toolset feature, IMO, and more about a generic - even above WordPress - question of the Web meanwhile.
Do you use archives or pages?
Do you use "logic" links or "doesn't matter, the title matters"?
I personally never used archives as they where (in past) a very minimal feature and completely useless to me.
Nowadays Toolset added a lot of features that let you style archives, turning them in easy to control, nice to have and find, "out of the box" kind of "View's" (for my usage cases).
As well users often when they find an interesting post, online, delete the "postname" in the URL so to reach the archive, in order to see if there is any other good stuff to read.
I guess that's a very common practice under more "development" related people but I have seen other people using this trick as well.
Here an Archive is the proper thing, they (visitors) will find all your posts there.
I suggest to have Views if you need 100% control over the putout.
Archives if you have/want them available (not everything can have an archive) and if you need just style and query control - but no deeper control with hooks, or nesting of Views, etc, and for an easy usage / presentation of content samples, leading to single posts.
I think another major benefit is SEO ranking, if you have accessible archives.
