aakk9999 - 12:13 pm on Jun 23, 2013 (gmt 0)
From what OP says, it can be concluded that the Site A is ranking mostly because of the great on-page SEO. So Robert's response is correct as all on-page SEO is lost with 301 Redirect.
If the Site A ranks primarily because of links (which is, btw, not what OP said), then the results of 301 can be unpredictable - it would depend on Site B pages' content, the power of links, whether the content of the each page on Site B is relevant to links received via redirect from Site A, etc. I think that in this case there is no "one size fits all" response.