Q:

今(temporal counter) vs. 本(temporal counter)

Aside from levels of formality, is there a difference in the meaning/nuance of

今日・今週・今月・今年 

as opposed to 

本日・本週・本月・本年

?

A:

本週 does not exist in the first place. BCCWJ returned virtually zero result, and there is no dictionary entry for 本週.
本月 is very rare. Most examples in BCCWJ are either from legal documents or quotes of old documents. I would say you should avoid using this term altogether unless you are a lawyer.
本年 and 本日 are relatively common and sound fairly formal and stiff. They are almost exclusively found in formal greetings, announcements and such. 今年/今日 are roughly 10 times more common than 本年/本日, according to the corpus. Grammatically speaking, I think there is no difference in usage; both are used either as nouns or as standalone adverbs. See also: What's the difference between 今日{きょう} and 本日{ほんじつ}?

