Hi Ash,
It's really a preference. The great thing about signing the blogs (rel=author) is you get the fancy picture in any results which can help you stand out a bit in the SERPs
I suppose you need to ask yourself what you want from Google+ you may find it easier to use the business account for brand announcements but the personal account for e.g blog posts. This may help you build up authority in your niche whilst keeping any +1 on your business page engaged. You can write (well comment) on your business page with your personal page to help reinforce. it's all far too overly complex if you ask me!
If I'm honest I'm not too familiar with duplicate content on social media but lets assume by duplicating it we lessen the value (and the impact). You could look on "sharing" the business post (or visa vesa I suppose) so the value all goes back to the same place.
In short if you work out what you think would benefit your brand you can then fit in the rest around it. I hope some of that helps anyway. Lets not forget Christy and her great suggestions you using your personal account to really contact with your niche.
Good Luck.