There's a few things to consider ...
The first thing I would ask is:
Have the articles already been published and been SEO'ed for the old company?
(i.e. backlinking, bookmarks, comment links, etc., all with keywords associated to the old company)
If so and if that company still gets search requests, then you may want to consider altering the existing content, where it is currently published, by changing the links and your call to action to reflect your new company as an alternative for people looking at the old company. This allows you to leverage an existing position rather than trying to establish a new one with the same content.
The key there really comes down to how evergreen the content is.
If it's too company specific I wouldn't focus on it right now and move on to creating content for the new company. Make sense?
If you're going to republish the content I would recommend at least a 50% rewrite, assuming it isn't too company specific; especially if the articles are already indexed. If the new product/service is similar,
a few changes should be sufficient; with new relevant content threaded into the old.
Among the top reasons is that ranking for the new company (i.e. needing to implement a fresh SEO campaign) if you want to do it the right way, will include the usual suspects such as backlinks, etc., that are optimized (anchor text etc.) with relevant keywords. The content itself (the articles) is going to need to contain these target keywords for the campaign to be as successful as possible.
For me, if I'm going to rewrite 50% I just take the extra initiative and write new content.
It's nearly the same effort, but I can approach the campaign with a fresh voice.
Use the old structure perhaps as a template if it ranked well.
The ideal scenario would be the ability to update the old content in its existing location, maintaining that position and rewriting (or creating new) for the new company, doubling your indexed content for the new company.
You could spin the old content, add new links and publish it, but I'm not an advocate of spinning.
I personally prefer 100% unique content with high quality links, published through a collection of top tier media outlets, rather than 1000s of low quality links.
Maybe someone else can add their thoughts on that.
Hope that helps.
If you have questions please do not hesitate to ask.