I think the best way to do this is to run both sites off 1 Joomla instal
You would have to spend some time aligning the data but once that is done then no more work is really needed.
The best way to do this is with 2 templates.
SiteA URL invokes templateA
SiteB URL invokes templateB
You can logically split the content using categories.
All content belonging to SiteA is in the SiteA category
All content belonging to SiteB is in the SiteB category
Assuming you are in a Joomla 1.7 or higher than you can split the permissions by giving the admin of siteA access to anything with the siteA category but if the admins can access all content then you don't have to do that.
I have a couple sites working this way and it is pretty seamless.