Hey there
Let's run through the two options and look at the pros and cons of each:
Moving content from old blog to new blog - if you do this, the first thing you'll want to do is remove the old content from the old blog, as you mentioned. This is to remove any chance of a duplicate content penalty.
Now, the links to your site from your old blog (plus any links to those blog posts) will be lost. You will know better than anyone if those links are high value or if they are nice authoritative links. You'd be losing those links in this method, but even if they were high quality I would be tempted to use this method anyway.
By having the blog content directly on your root domain, there's nothing stopping from high authority websites linking to those posts in the future, particularly if the content is timeless. That means you'd be getting the benefit of those links directly to your site.
As a contingency, if you find any links pointing to your old blog and would like to keep them, reaching out to the webmaster who owns the site is a good idea. I'm sure they'd be keen on not sending their own users to a 404 page as it makes them look bad. Tell them you've updated the URL and you can keep the link.
As for the other option - keeping the old blog and starting fresh with the new one. This will make your new blog appear sparse at first, which isn't that bad of a thing and certainly not from an SEO perspective. You'd be keeping the links from the old blog to your site in this sense, but the only problem is that if people want to link to your old blog posts, you're not getting the direct benefit of that to your new domain. The strength of that link will be diluted somewhat.
On a personal note, I always prefer keeping your content on your main site for contingency reasons anyway. I want my site, or whichever site I'm working on, to be the number 1 stop for users looking for information, resources, tools, advice etc. For that reason, I'd go with option one and take the necessary steps outlined above.
Hope this helps.