I also will suggest you the same as above : yoursite/blog.com. Because it is common to have URL like this and I have rarely seen URL like blog/yoursite.com .
Also you may also want to have your blog's topic as a subdirectory for yoursite.com. For example, if you have a finance site, you may want to make it yoursite.com/finance. Finance which is your blog. This can add additional spider food because they already know that your site is all about finance.
Here will come the benefit if you have researched a keyword like "finance checklist guides" then your url would be "yoursite.com/finance/finance-checklist-guides" the word "finance" alone is mentioned 2x in the url so that would give additional point for your SEO. Not that much but very effective.
Blog.com is already registered so if you want to use that you have to open an account and use their hosting and you have no control. If you do blog.yoursite.com then you can host it yourself and you have control.
either one is fine. I used to run a blog on a subdomain for a company and I was quite fond of the neatness of the domain name. Totally unnecessary though, site.com/blog will be fine.
Also you may also want to have your blog's topic as a subdirectory for yoursite.com. For example, if you have a finance site, you may want to make it yoursite.com/finance. Finance which is your blog. This can add additional spider food because they already know that your site is all about finance.
Here will come the benefit if you have researched a keyword like "finance checklist guides" then your url would be "yoursite.com/finance/finance-checklist-guides" the word "finance" alone is mentioned 2x in the url so that would give additional point for your SEO. Not that much but very effective.
yoursite.com/blog is better, because if you promote it, you'll get more backlinks to your main domain, instead of trying to build backlinks to a new subdomain.